# Svante Janson

Professor at Department of Mathematics; Probability Theory and Combinatorics

- Telephone:
- +46 18 471 31 88
- E-mail:
- Svante.Janson@math.uu.se
- Visiting address:
- Ångströmlaboratoriet, Lägerhyddsvägen 1
- Postal address:
- Box 480

751 06 UPPSALA

- Academic merits:
- PhD
- CV:
- Download CV

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## Short presentation

My research is mainly in probability theory, in particular combinatorial probability (mainly random graphs and related topics); occasionally I also do research in analysis, which was my original field.

I have written 4 books and over 300 journal papers. See my list of publications, which also includes a list of my coauthors in alphabetic order.

See also the list of some of my talks.

## Biography

I am member of The Royal Swedish Academy of Sciences, The Royal Society of Sciences at Uppsala, The Swedish Mathematical Society , Svenska statistikfrämjandet, Vetenskap och Folkbildning.

I am, besides my research, interested in calendars and their mathematics and election methods.

I have earlier participated in, and helped launching, the project Samnordisk runtextdatabas (a data base with runic texts).

Awards:

- Sparre's prize (KVA) 1978
- Göran Gustafsson prize 1992
- Eva och Lars Gårding's prize (Kungl. Fysiografiska sällskapet i Lund) 2009
- Wallenberg Scholar (The Knut and Alice Wallenberg Foundation) 2011
- Rudbeck medal (Uppsala University) 2013
- Celsius medal (Royal Society of Sciences at Uppsala) 2016

My family consists of my wife fru Julie White and our daughter Sofie (born 1995), and our "extra children" Erika (born 1979), Magnus (born 1980), Emma (born 1987), and Jesper (born 1981) that occasionally have lived with us as children.

## Publications

### Recent publications

- Phragmén's voting methods and justified representation (2024)
- Identities and periodic oscillations of divide-and-conquer recurrences splitting at half (2024)
- On a central limit theorem in renewal theory (2024)
- The number of descendants in a random directed acyclic graph (2024)
- Quantitative bounds in the central limit theorem for
*m*-dependent random variables (2024)

### All publications

#### Articles

- Phragmén's voting methods and justified representation (2024)
- Identities and periodic oscillations of divide-and-conquer recurrences splitting at half (2024)
- On a central limit theorem in renewal theory (2024)
- The number of descendants in a random directed acyclic graph (2024)
- Quantitative bounds in the central limit theorem for
*m*-dependent random variables (2024) - Fluctuations of subgraph counts in graphon based random graphs (2023)
- The number of occurrences of patterns in a random tree or forest permutation (2023)
- Asymptotic normality for
*M*-dependent and constrained*U*-statistics, with applications to pattern matching in random strings and permutations (2023) - Estimating global subgraph counts by sampling (2023)
- Unicellular maps vs. hyperbolic surfaces in large genus (2023)
- Fluctuations of balanced urns with infinitely many colours (2023)
- The distance profile of rooted and unrooted simply generated trees (2022)
- The sum of powers of subtree sizes for conditioned Galton-Watson trees (2022)
- Minimal matchings of point processes (2022)
- Central limit theorems for additive functionals and fringe trees in tries (2022)
- On convergence for graphexes (2022)
- Short cycles in high genus unicellular maps (2022)
- Successive minimum spanning trees (2022)
- Continuous-time digital search tree and a border aggregation model (2022)
- TO FIXATE OR NOT TO FIXATE IN TWO-TYPE ANNIHILATING BRANCHING RANDOM WALKS (2021)
- A.s. convergence for infinite colour Pólya urns associated with random walks (2021)
- The Space D in Several Variables (2021)
- On distance covariance in metric and Hilbert spaces (2021)
- Tree limits and limits of random trees (2021)
- On the probability that a binomial variable is at most its expectation (2021)
- On general subtrees of a conditioned Galton-Watson tree (2021)
- Tensor norms on ordered normed spaces, polarization constants, and exchangeable distributions (2021)
- Hidden Words Statistics for Large Patterns (2021)
- Preferential attachment without vertex growth (2021)
- Strong convergence of infinite color balanced urns under uniform ergodicity (2020)
- Patterns in Random Permutations Avoiding Some Sets of Multiple Patterns (2020)
- A graphon counter example (2020)
- Random graphs with given vertex degrees and switchings (2020)
- Rate of convergence for traditional Polya urns (2020)
- Mean and variance of balanced Pólya urns (2020)
- Asymptotic normality in random graphs with given vertex degrees (2020)
- On the independence number of some random trees (2020)
- Competing first passage percolation on random graphs with finite variance degrees (2019)
- Competition in growth and urns (2019)
- Inversions in Split Trees and Conditional Galton-Watson Treest (2019)
- Random Recursive Trees and Preferential Attachment Trees are Random Split Trees (2019)
- Patterns in random permutations avoiding the pattern 321 (2019)
- The hiring problem with rank-based strategies (2019)
- Random replacements in Polya urns with infinitely many colours (2019)
- A modified bootstrap percolation on a random graph coupled with a lattice (2019)
- Preferential attachment when stable (2019)
- Long Term Behaviour of a Reversible System of Interacting Random Walks (2019)
- A piecewise contractive dynamical system and Phragmèn's election method (2019)
- Component structure of the configuration model (2019)
- Non-fringe subtrees in conditioned Galton-Watson trees (2018)
- Graph properties, graph limits, and entropy (2018)
- Tail bounds for sums of geometric and exponential variables (2018)
- On Edge Exchangeable Random Graphs (2018)
- Asymptotics Of Fluctuations In Crump-Mode-Jagers Processes (2018)
- Renewal theory for asymmetric U-statistics (2018)
- Moment convergence of balanced Polya processes (2018)
- Sesqui-type branching processes (2018)
- On the critical probability in percolation (2018)
- Packing Random Graphs and Hypergraphs (2017)
- The Greedy Independent Set in a Random Graph with Given Degrees (2017)
- Fringe trees, Crump-Mode-Jagers branching processes and
*m*-ary search trees (2017) - Multivariate normal limit laws for the numbers of fringe subtrees in m-ary search trees and preferential attachment trees (2017)
- Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half (2017)
- Patterns in Random Permutations Avoiding the Pattern 132 (2017)
- Near-critical SIR epidemic on a random graph with given degrees (2017)
- On String Graph Limits and the Structure of a Typical String Graph (2017)
- On the Length of a Random Minimum Spanning Tree (2016)
- The inverse first-passage problem and optimal stopping (2016)
- Influence in product spaces (2016)
- Asymptotic Normality of Fringe Subtrees and Additive Functionals in Conditioned Galton-Watson Trees (2016)
- Graph limits and hereditary properties (2016)
- On a representation theorem for finitely exchangeable random vectors (2016)
- A Unified Approach to Linear Probing Hashing with Buckets (2016)
- The lower tail (2016)
- Feynman-Kac Theorems for Generalized Diffusions (2015)
- Asymptotic distribution of two-protected nodes in ternary search trees (2015)
- Limit laws for functions of fringe trees for binary search trees and random recursive trees (2015)
- Superboolean rank and the size of the largest triangular submatrix of a random matrix (2015)
- Asymptotic Distribution Of The Maximum Interpoint Distance In A Sample Of Random Vectors With A Spherically Symmetric Distribution (2015)
- ON DEGENERATE SUMS OF m-DEPENDENT VARIABLES (2015)
- Maximal clades in random binary search trees (2015)
- On the tails of the limiting Quicksort distribution (2015)
- Higher moments of Banach space valued random variables (2015)
- On the asymptotic statistics of the number of occurrences of multiple permutation patterns (2015)
- More on quasi-random graphs, subgraph counts and graph limits (2015)
- Scaling limits of random planar maps with a unique large face (2015)
- On the Spread of Random Graphs (2014)
- First critical probability for a problem on random orientations in G(n,p) (2014)
- Bootstrap percolation on Galton-Watson trees (2014)
- Protected nodes and fringe subtrees in some random trees (2014)
- Graphs where every k-subset of vertices is an identifying set (2014)
- Weighted Random Staircase Tableaux (2014)
- The probability that a rqandom multigraph is simple II (2014)
- Asymptotic bias of some election methods (2014)
- Law of Large Numbers for the SIR Epidemic on a Random Graph with Given Degrees (2014)
- On the Typical Structure of Graphs in a Monotone Property (2014)
- On Symmetry of Uniform and Preferential Attachment Graphs (2014)
- Sub-Gaussian tail bounds for the width and height of conditioned Galton–Watson trees (2013)
- Interval Graph Limits (2013)
- Note on a partition limit theorem for rank and crank (2013)
- Can time-homogeneous diffusions produce any distribution? (2013)
- Moments of the location of the maximum of Brownian motion with parabolic drift (2013)
- Euler-Frobenius numbers and rounding (2013)
- Graphons, cut norm and distance, couplings and rearrangements (2013)
- An example of graph limits of growing sequences of random graphs (2013)
- Coupon collecting and transversals of hypergraphs (2013)
- Monotone graph limits and quasimonotone graphs (2012)
- The number of bit comparisons used by Quicksort (2012)
- Partitions with Distinct Multiplicities of Parts (2012)
- Generalized Galois numbers, inversions, lattice paths, Ferrers diagrams and limit theorems (2012)
- Renewal theory in the analysis of tries and strings (2012)
- Simply generated trees, conditioned Galton-Watson trees, random allocations and condensation (2012)
- The probability of the Alabama paradox (2012)
- Bootstrap percolation on the random graph Gn,p (2012)
- Hitting Times for Random Walks with Restarts (2012)
- Susceptibility in inhomogeneous random graphs (2012)
- Phase transitions for modified Erdős–Rényi processes (2012)
- Correlations for Paths in Random Orientations of G(n, p) and G(n, m) (2011)
- On Vertex, Edge, and Vertex-Edge Random Graphs (2011)
- Sparse Random Graphs with Clustering (2011)
- On Covering by Translates of a Set (2011)
- The Mahonian probability distribution on words is asymptotically normal (2011)
- Distances Between Pairs of Vertices and Vertical Profile in Conditioned Galton-Watson Trees (2011)
- Long and short paths in uniform random recursive dags (2011)
- A central limit theorem for random ordered factorizations of integers (2011)
- Networking - smoothly does it (2011)
- Poset limits and exchangeable random posets (2011)
- Quasi-random graphs and graph limits (2011)
- Random trees with superexponential branching weights (2011)
- On the total external length of the Kingman coalescent (2011)
- Generalized Stirling permutations, families of increasing trees and urn models (2011)
- Absolutely continuous compensators (2011)
- Duality in Inhomogeneous Random Graphs, and the Cut Metric (2011)
- Upper tails for counting objects in randomly induced subhypergraphs and rooted random graphs (2011)
- The Cut Metric, Random Graphs, and Branching Processes (2010)
- On the Number of Perfect Matchings in Random Lifts (2010)
- Random Graphs with Forbidden Vertex Degrees (2010)
- Susceptibility of random graphs with given vertex degrees (2010)
- Asymptotic Equivalence and Contiguity of Some Random Graphs (2010)
- Moments of gamma type and the Brownian supremum process area (2010)
- A divergent generating function that can be summed and analysed analytically (2010)
- The maximum of Brownian motion with parabolic drift (2010)
- Large cliques in a power-law random graph (2010)
- A functional combinatorial central limit theorem (2009)
- Line-of-sight percolation (2009)
- Precise logarithmic asymptotics for the right tails of some limit random variables for random trees (2009)
- Random even graphs (2009)
- On percolation in random graphs with given vertex degrees (2009)
- Sorting using complete subintervals and the maximum number of runs in a randomly evolving sequence (2009)
- The probability that a random multigraph is simple (2009)
- Standard representation of multivariate functions on a general probability space (2009)
- On the size of identifying codes in binary hypercubes (2009)
- A new approach to the giant component problem (2009)
- Zeros of sections of the binomial expansion (2009)
- Threshold graph limits and random threshold graphs (2008)
- A functional limit theorem for the profile of search trees (2008)
- Local limit theorems for finite and infinite urn models (2008)
- Individual displacements in hashing with coalesced chains (2008)
- On the asymptotic joint distribution of height and width in random trees (2008)
- The largest component in a subcritical random graph with a power law degree distribution (2008)
- Graph limits and exchangeable random graphs (2008)
- Convergence of some leader election algorithms (2008)
- Susceptibility in subcritical random graphs (2008)
- Asymptotic normality of the k-core in random graphs (2008)
- The size of random fragmentation trees (2008)
- Dismantling sparse random graphs (2008)
- Spread-out percolation in R-d (2007)
- The phase transition in inhomogeneous random graphs (2007)
- Graphs with specified degree distributions, simple epidemics and local vaccination strategies (2007)
- On a random graph related to quantum theory (2007)
- Monotonicity, asymptotic normality and vertex degrees in random graphs (2007)
- Brownian excursion area, Wright's constants in graph enumeration, and other Brownian areas (2007)
- Tail estimates for the Brownian excursion area and other Brownian areas (2007)
- A simple solution to the k-core problem (2007)
- A point process describing the component sizes in the critical window of the random graph evolution (2007)
- Partial fillup and search time in LC tries (2007)
- Rainbow Hamilton cycles in random regular graphs (2007)
- The mean, variance and limiting distribution of two statistics sensitive to phylogenetic tree balance (2006)
- The density of the ISE and local limit laws for embedded trees (2006)
- Congruence properties of depths in some random trees (2006)
- Left and right pathlengths in random binary trees (2006)
- Random cutting and records in deterministic and random trees (2006)
- Rounding of continuous random variables and oscillatory asymptotics (2006)
- Feynman-Kac formulas for Black-Scholes type operators (2006)
- Superreplication of options on several underlying assets (2005)
- Individual displacements for linear probing hashing with different insertion policies. (2005)
- Asymptotic degree distribution in random recursive trees (2005)
- The first eigenvalue of random graphs (2005)
- Limit theorems for triangular urn schemes (2005)
- The phase transition in the uniformly grown random graph has infinite order (2005)
- Convergence of coined quantum walks on R^d (2005)
- Branching processes, and random-cluster measures on trees. (2005)
- Convergence of discrete snakes (2005)
- Some remarks on the combinatorics of IS_n (2005)
- Large deviations for sums of partly dependent random variables (2004)
- One-sided interval trees (2004)
- Functional limit theorems for multitype branching processes (2004)
- Rademacher chaos: tail estimates vs limit theorems (2004)
- The center of mass of the ISE and the Wiener index of trees (2004)
- On generalized random railways (2004)
- Weak limits for quantum random walks (2004)
- On the average sequence complexity (2004)
- Robust reconstruction on trees is determined by the second eigenvalue (2004)
- Upper tails for subgraph counts in random graphs (2004)
- The deletion method for upper tail estimates. (2004)
- Preservation of convexity of solutions to parabolic equations (2004)
- Approximation of subgraph counts in the uniform attachment model

#### Conferences

- Phragmen's Voting Methods and Justified Representation (2017)
- Asymptotic normality of statistics on permutation tableaux (2010)
- Plane recursive trees, Stirling permutations and an urn model (2008)
- Complex interpolation of compact operators into the couple (FL^oo,FL_1^oo) (2007)
- Sorting using complete subintervals and the maximum number of runs in a randomly evolving sequence (2007)
- Conditioned Galton-Watson trees do not grow (2006)
- Random records and cuttings in complete binary trees (2004)
- The number of bit comparisons used by Quicksort: an average-case analysis (2004)

#### Reports

- Proportionella val inom kommunfullmäktige (2019)
- Graphons, cut norm and distance, couplings and rearrangements (2010)
- Moments of Gamma type and the Brownian supremum process area (2010)
- Sub-Gaussian tail bounds for the width and height of conditioned Galton–Watson trees (2010)
- The maximum of Brownian motion with parabolic drift (2010)
- Bootstrap percolation on the random graph G
,*n*(2010)*p* - Absolutely Continuous Compensators (2010)
- Hitting times for random walks with restarts (2010)
- Phase transitions for modified Erdös-Rényi processes (2010)
- Renewal theory in analysis of tries and string (2009)
- ON THE SPREAD OF SUPERCRITICAL RANDOM GRAPHS (2009)
- The cut metric, random graphs, and branching processes (2009)
- On covering by translates of a set (2009)
- THE MAHONIAN PROBABILITY DISTRIBUTION ON WORDS IS ASYMPTOTICALLY NORMAL (2009)
- Graphs where every k-subset of vertices is an identifying set (2009)
- Zeros of Sections of the Binomial Expansion (2009)
- Plane recursive trees, stirling permutations and an urn model (2008)
- On percolation in random graphs with given vertex degrees (2008)
- Connectedness in graph limits (2008)
- Standard representation of multivariate functions on a general probability space (2008)
- Asymptotic equivalence and contiguity of some random graphs (2008)
- On vertex, edge, and vertex-edge random graph (2008)
- Sparse random graphs with clustering (2008)
- Distances between pairs of vertices and vertical profile in conditioned galton–watson tree (2008)
- Generalized stirling permutations, families of increasing trees and urn models (2008)
- On the Size of Identifying Codes in Binary Hypercubes (2008)
- Convergence of some leader election algorithms (2008)
- Susceptibility in subcritical random graph (2008)
- Line-of-sight percolation (2007)
- Graphs with specified degree distributions, simple epidemics and local vaccination strategies (2007)
- Graph limits and exchangeable random graphs (2007)
- Precise logarithmic asymptotics for the right tails of some limit random variables for random trees (2007)
- Random even graphs and the Ising model (2007)
- Random graphs with forbidden vertex degrees (2007)
- Standard representation of multivariate functions on a general probability space (2007)
- Sorting using complete subintervals and the maximum number of runs in a randomly evolving sequence (2007)
- The largest component in a subcritical random graph with a power law degree distribution (2007)
- Tail estimates for the Brownian excursion area and other Brownian areas (2007)
- A new approach to the giant component problem (2007)
- Asymptotic normality of the k-core in random graphs (2007)
- The integral of the supremum process of Brownian motion (2007)
- Dismantling sparse random graphs (2007)
- A Functional Limit Theorem for The Profile of Search Trees (2006)
- Local limit theorems for finite and infinite urn models (2006)
- On a random graph related to quantum theory (2006)
- Monotonicity, asymptotic normality and vertex degrees in random graphs (2006)
- The probability that a random multigraph is simple (2006)
- Congruence properties of depths in some random trees (2005)
- Individual displacements in hashing with coalesced chains (2005)
- The phase transition in inhomogeneous random graphs (2005)
- The density of the ISE and local limit laws for embedded trees (2005)
- A simple solution to the k-core problem (2005)
- A point process describing the component sizes in the critical window of the random graph evolution (2005)
- Partial Fillup and Search Time in LC Tries (2005)
- Rainbow Hamilton cycles in random regular graphs (2005)
- Left and right pathlenghts in random binary trees (2004)
- Rounding of continuous random variables and oscillatory asymptotics (2004)
- Branching processes, and random-cluster measures on trees (2004)
- Random cutting and records in deterministic and random trees (2004)
- Limit theorems for triangular urn schemes (2004)
- On the asymptotic joint distribution of height and width in random trees (2004)
- Convergence of coined quantum walks on R^d (2004)
- Some remarks on the combinatorics of ISn (2004)
- Feynman-Kac formulas for Black-Scholes type operators (2004)
- Superreplication of options on several underlying assets (2003)
- Weak limits for quantum random walks (2003)
- Asymptotic degree distribution in random recursive trees (2003)
- Functional limit theorems for multitype branching processes and generalized Pólya urns (2003)
- One-sided interval trees (2003)
- The first eigenvalue of random graphs (2003)
- Individual displacements for linear probing hashing with different insertion policies (2003)
- Sorting with unreliable comparisons: a probabilistic analysis (2003)
- The center of mass of the ISE and the Wiener index of trees (2003)
- Preservation of Convexity of Solutions to Parabolic Equations (2003)
- On the average sequence complexity (2003)