Dr. Jan M. Swart
head of the department

Biography
Publication list
I was born 1970 in Drachten, the Netherlands, and studied theoretical physics at Groningen University from 1988-1994. From 1995-1999 I did my PhD in mathematics at Nijmegen University under the supervision of Frank den Hollander (thesis: Large Space-Time Scale Behavior of Linearly Interacting Diffusions). Between 1999 and 2005 I held postdoc positions at the TU Berlin (18 months), Erlangen (4 years) and Tübingen (the final 6 months). I obtained my habilitation at the University of Erlangen-Nuremberg in 2007 (thesis: Extinction versus unbounded growth). Since 2005 I have been at the Institute of Information Theory and Automatization of the Academy of Sciences of the Czech Republic, Prague.
My research interests lie in probability theory, more specifically in the general area of interacting particle systems, percolation, and other models for space-time randomness with strong correlations. While much of the original impetus for studying these models came from theoretical physics, many of the models I have occupied myself with are (at least in part) motivated by problems from (population) biology. Since explicit solutions are usually not available, the art is to find methods that lead to good qualitative or approximative statements about these models. I am co-inventor of the Brownian net, a continuum model of branching and coalescing Browian motions.
Since 2007, I have usually taught one course each semester at Charles University on topics such as Interacting Particle Systems, Quantum Probability, Markov Chains, Large Deviations, Percolation, and Random Graphs. My lecture notes on Interacting Particle Systems are on the arXiv.
Books and chapters
- The Algebraic Approach to Duality: An Introduction, Genealogies of Interacting Particle Systems, p. 81-150, Hackensack: World Scientific (New Jersey, 2020) Download DOI: 10.1142/9789811206092_0003 [2020] :
- The Brownian web, the Brownian net, and their universality, Advances in Disordered Systems, Random Processes and Some Applications, p. 270-368, Eds: Contucci Pierluigi, Giardina Cristian Download DOI: 10.1017/9781316403877.007 [2016] :
Journal articles
- Weaves, webs and flows, Electronic Journal of Probability 29 1 (2024), p. 1-82 Download Download DOI: 10.1214/24-EJP1161 [2024] :
- Applying monoid duality to a double contact process, Electronic Journal of Probability 28 Download Download DOI: 10.1214/23-EJP961 [2023] :
- Commutative monoid duality, Journal of Theoretical Probability 36 2 (2023), p. 1088-1115 Download Download DOI: 10.1007/s10959-022-01197-7 [2023] :
- A phase transition between endogeny and nonendogeny, Electronic Journal of Probability 27 Download Download DOI: 10.1214/22-EJP872 [2022] :
- Frozen percolation on the binary tree is nonendogenous, Annals of Probability 49 5 (2021), p. 2272-2316 Download Download DOI: 10.1214/21-AOP1507 [2021] :
- An invariance principle for biased voter model interfaces, Bernoulli 27 1 (2021), p. 615-636 Download Download DOI: 10.3150/20-BEJ1252 [2021] :
- Recursive tree processes and the mean-field limit of stochastic flows, Electronic Journal of Probability 25 Download Download DOI: 10.1214/20-EJP460 [2020] :
- Equilibrium interfaces of biased voter models, Annals of Applied Probability 29 4 (2019), p. 2556-2593 Download Download DOI: 10.1214/19-AAP1461 [2019] :
- How much market making does a market need?, Journal of Applied Probability 55 3 (2018), p. 667-681 Download DOI: 10.1017/jpr.2018.44 [2018] :
- A new characterization of endogeny, Mathematical Physics, Analysis and Geometry 21 Download DOI: 10.1007/s11040-018-9288-y [2018] :
- Rigorous results for the Stigler-Luckock model for the evolution of an order book, Annals of Applied Probability 28 3 (2018), p. 1491-1535 Download DOI: 10.1214/17-AAP1336 [2018] :
- Pathwise duals of monotone and additive Markov processes, Journal of Theoretical Probability 31 2 (2018), p. 932-983 Download DOI: 10.1007/s10959-016-0721-5 [2018] :
- A simple proof of exponential decay of subcritical contact processes, Probability Theory and Related Fields 170, p. 1-9 Download DOI: 10.1007/s00440-016-0741-1 [2018] :
- A simple rank-based Markov chain with self-organized criticality, Markov Processes and Related Fields 23 1 (2017), p. 87-102 Download [2017] :
- The limiting shape of a full mailbox, Alea (Rio de Janeiro) 13 2 (2016), p. 1151-1164 Download [2016] :
- A particle system with cooperative branching and coalescence, Annals of Applied Probability 25 3 (2015), p. 1616-1649 Download DOI: 10.1214/14-AAP1032 [2015] :
- Entropy-driven phase transition in low-temperature antiferromagnetic Potts models, Communications in Mathematical Physics 330 3 (2014), p. 1339-1394 Download DOI: 10.1007/s00220-014-2005-1 [2014] :
- Subcritical contact processes seen from a typical infected site, Electronic Journal of Probability 19 1 (2014) Download DOI: 10.1214/EJP.v19-2904 [2014] :
- Stochastic flows in the Brownian web and net, Memoirs of the American Mathematical Society 227 1065 (2014), p. 1-160 Download DOI: 10.1090/S0065-9266-2013-00687-9 [2014] :
- Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q, Physical Review E 87 Download DOI: 10.1103/PhysRevE.87.012136 [2013] :
- Noninvadability implies noncoexistence for a class of cancellative systems, Electronic Communications in Probability 18 38 (2013), p. 1-12 Download DOI: 10.1214/ECP.v18-2471 [2013] :
- Systems of branching, annihilating, and coalescing particles, Electronic Journal of Probability 17 80 (2012), p. 1-32 Download DOI: 10.1214/EJP.v17-2003 [2012] :
- Intertwining of birth-and-death processes, Kybernetika 47 1 (2011), p. 1-14 Download [2011] :
- Numerical analysis of the rebellious voter model, Journal of Statistical Physics 140 5 (2010), p. 873-899 Download DOI: 10.1007/s10955-010-0021-x [2010] :
- Survival of contact processes on the hierarchical group, Probability Theory and Related Fields 147 3 (2010), p. 529-563 Download DOI: 10.1007/s00440-009-0214-x [2010] :
- The contact process seen from a typical infected site, Journal of Theoretical Probability 22 3 (2009), p. 711-740 Download DOI: 10.1007/s10959-008-0184-4 [2009] :
- Special points of the Brownian net, Electronic Journal of Probability 14, p. 805-864 Download [2009] :
- The renormalization transformation for two-type branching models, Annales de L Institut Henri Poincare-Probabilites Et Statistiques 44 6 (2008), p. 1038-1077 Download DOI: 10.1214/07-AIHP143 [2008] :
- Tightness of voter model interfaces, Electronic Communications in Probability 13, p. 165-174 Download [2008] :
- The Brownian net, Annals of Probability 36 3 (2008), p. 1153-1208 [2008] :
- Voter models with heterozygosity selection, Annals of Applied Probability 18 1 (2008), p. 59-99 DOI: 10.1214/07-AAP444 [2008] :
- Renormalization analysis of catalytic Wright-Fisher diffusions, Electronic Journal of Probability 2006 11 (2006), p. 585-654 [2006] :
Other publications
- Learning Sessions: more work, less shop?, IMS Bulletin 46 7 (2017), p. 16-17 Download [2017] :
- Numerical Analysis of the Rebellious Voter Model, Abstracts of Contributions to 7th International Workshop on Data - Algorithms - Decision Making, p. 48-48, Eds: Janžura M., Ivánek J. Download [2011] :
- Duals and thinnings of some relatives of the contact process, Prague Stochastics 2006, p. 1-12, Eds: Hušková M., Janžura M. [2006] :