Jan Swart - Preprints


ORCID: 0000-0001-8614-4053  ResearcherID: G-7286-2014.

My Doctoral Thesis

My Habilitation Thesis arXiv:math.PR/0702095


Preprints

  1. R. Sun, J.M. Swart, and J. Yu (2024): Universality of the Brownian net. ArXiv:2401.09370.
  2. J.N. Latz and J.M. Swart (2023): Monotone duality of interacting particle systems. ArXiv:2312.00595 .
  3. N. Freeman and J. Swart (2023): Weaves, webs and flows . ArXiv:2302.02773 .
  4. N. Freeman and J.M. Swart (2022): Skorohod's topologies on path space. ArXiv:2301.05637.
  5. J.N. Latz and J.M. Swart (2022): Applying monoid duality to a double contact process. (Electron. J. Probab. 28 (2023), paper no. 70, 1-26.) ArXiv:2209.06017. (Here is the first version.)
  6. J.M. Swart, R. Szabó, and C. Toninelli. (2022): Peierls bounds from Toom contours. ArXiv:2202.10999.
  7. J.N. Latz and J.M. Swart. (2021): Commutative monoid duality. (J. Theor. Probab. 36 (2023) 1088-1115. view online) ArXiv:2108.01492. (Here are the first and second version.)
  8. B. Ráth, J.M. Swart, and M. Szőke. (2021): A phase transition between endogeny and nonendogeny. (Electron. J. Probab. 27 (2022) paper No. 145, 1-43) ArXiv:2103.14408. (Here is the first version.)
  9. B. Ráth, J.M. Swart, and T. Terpai (2019): Frozen percolation on the binary tree is nonendogenous. (Ann. Probab. 49(5) (2021), 2272-2316.) ArXiv:1910.09213. (Here are the first, second, and final version.)
  10. R. Sun, J.M. Swart, and J. Yu (2019): An invariance principle for biased voter model interfaces. (Bernoulli 27(1) (2021) 615-636) ArXiv:1908.02944. (Here are the first and second versions.)
  11. T. Mach, A. Sturm, and J.M. Swart (2018): Recursive tree processes and the mean-field limit of stochastic flows. (Electron. J. Probab. 25 (2020) paper No. 61, 1-63) ArXiv:1812.10787. (Here is the first version.)
  12. R. Sun, J.M. Swart, and J. Yu (2018): Equilibrium interfaces of biased voter models. (Ann. Appl. Probab. 29(4) (2019), 2556-2593.) ArXiv:1804.04342. (Here is the first version.)
  13. T. Mach, A. Sturm, and J.M. Swart (2018): A new characterization of endogeny. (Math. Phys. Anal. Geom. 21(4) (2018), paper no. 30, 19 pages.) (!) ArXiv:1801.05253. (Here are the first and second versions.)
  14. J.M. Swart (2017): Necessary and sufficient conditions for a nonnegative matrix to be strongly R-positive. ArXiv:1709.09459. (Here is the first version.)
  15. V. Peržina and J.M. Swart (2016): How much market making does a market need?. (J. Appl. Probab. 55(3) (2018), 667-681. (!) Doi 10.1017/jpr.2018.44) ArXiv:1612.00981. (Here are the first and second versions.)
  16. J.M. Swart (2016): Rigorous results for the Stigler-Luckock model for the evolution of an order book. (Ann. Appl. Probab. 28(3) (2018), 1491-1535) ArXiv:1605.01551. (Here are the original and corrected preprint.)
  17. J.M. Swart (2016): A simple proof of exponential decay of subcritical contact processes. (Probab. Theory Relat. Fields 170(1/2) (2018) 1-9.; see also here) ArXiv:1603.09142. (Here is the first version.)
  18. E. Schertzer, R. Sun and J.M. Swart. The Brownian Web, the Brownian Net, and their Universality. (Lecture notes from a trimester program at the Institut Henri Poincaré, Jan 5 - Apr 3, 2015.) Published as pages 270-368 in: P. Contucci and C. Giardinà (Eds.) Advances in Disordered Systems, Random Processes and Some Applications, Cambridge University Press, ISBN 9781107124103, 2016. ArXiv:1506.00724.
  19. M. Formentin and J.M. Swart (2015): The limiting shape of a full mailbox. (ALEA 13(2) (2016) 1151-1164) ArXiv:1511.04261. (Here is the first version.)
  20. A. Sturm and J.M. Swart (2015): Pathwise duals of monotone and additive Markov processes. (J. Theor. Probab. 31(2) (2018), 932-983. view online) ArXiv:1510.06284. (Here is the first version.)
  21. J.M. Swart (2014): A simple rank-based Markov chain with self-organized criticality. (Markov Process. Related Fields 23(1) (2017), 87-102.) ArXiv:1405.3609. (Here are the first and second versions.) Remark: The model in this paper has independently been reinvented by D. Fraiman in this paper (see also arXiv:1805.09763).
  22. A. Sturm and J.M. Swart (2013): A particle system with cooperative branching and coalescence. (Ann. Appl. Probab. 25(3) (2015), 1616-1649) ArXiv:1311.0417v3. (Here are the original and corrected preprints.)
  23. J.M. Swart (2012): Noninvadability implies noncoexistence for a class of cancellative systems. (Electron. Commun. Probab. 18 (2013) paper No. 38, 1-12) ArXiv:1211.7178v2. (Here is the original version.)
  24. Y. Huang, K. Chen, Y. Deng, J.L. Jacobsen, R. Kotecký, J. Salas, A.D. Sokal, and J.M. Swart (2012): Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q. (Phys. Rev. E, 87(1) (2013), p.012136) ArXiv:1210.6248v1.
  25. R. Kotecký, Alan D. Sokal and Jan M. Swart (2013): Entropy-driven phase transition in low-temperature antiferromagnetic Potts models. (Commun. Math. Phys. 330(3) (2014), 1339-1394) ArXiv:1205.4472v1. (Here is the first version.)
  26. S.R. Athreya and J.M. Swart (2012): Systems of branching, annihilating, and coalescing particles. (Electron. J. Probab. 17 (2012) paper No. 80, 1-32) ArXiv:1203.6477.
  27. A. Sturm and J.M. Swart (2011): Subcritical contact processes seen from a typical infected site. (Electron. J. Probab. 19 (2014), no. 53, 1-46.) ArXiv:1110.4777v3. (This is the second revision. Here are the second and first version.) Remark: some of the results of this paper were simultaneously proved by different means in E. Andjel, F. Ezanno, P. Groisman, and L. Rolla. Subcritical contact process seen from the edge: convergence to quasi-equilibrium. (Electron. J. Probab. 20 (2015), no. 32, 1-16.)
  28. E. Schertzer, R. Sun and J.M. Swart (2010): Stochastic flows in the Brownian web and net. (Mem. Am. Math. Soc. Vol. 227 (2014), Nr. 1065). Here is a corrected version of Appendix B, that in the published version contains some minor errors. ArXiv:1011.389v2. Here is the first version
  29. J.M. Swart (2010): Intertwining of birth-and-death processes (Kybernetika 47 No. 1 (2011) 1-14). ArXiv:1004.5515. Here is the first version
  30. J.M. Swart and K. Vrbenský (2009): Numerical analysis of the rebellious voter model (J. Stat. Phys. 140(5) (2010) 873-899) ("The final publication is available at www.springerlink.com") ArXiv:0911.1266v3. Here are a black and white version of the manuscript for printing and the raw data and variables plotted in the figures. Here are the second version, its b/w version and data, as well as the first version, its b/w version and data.
  31. S.R. Athreya and J.M. Swart (2008): Survival of contact processes on the hierarchical group. (Prob. Theory Relat. Fields 147 No. 3 (2010), 529-563), arXiv:0808.3732v3. Here are the second version and the original preprint.
  32. E. Schertzer, R. Sun and J.M. Swart (2008): Special points of the Brownian net. (Electron. J. Probab. 14 (2009) paper No. 30, 805-864) arXiv:0806.2326v2. Here is the original preprint
  33. A. Sturm and J.M. Swart (2007): Tightness of voter model interfaces. (Electron. Commun. Probab. 13 (2008) paper No. 16, 165-174) arXiv:0706.4405v2. Correction: in the published version, in (3.30), the infimum should be a supremum. The final version corrects a serious error in Lemma 3 of the original preprint.
  34. A. Sturm and J.M. Swart (2007): Voter models with heterozygosity selection. (Ann. Appl. Probab. 18 No. 1 (2008), 59-99) arXiv:math.PR/0701555v2. Here are the original preprint and the final version.
  35. D.A. Dawson, A. Greven, F. den Hollander, R. Sun, and J.M. Swart (2006): The renormalization transformation for two-type branching models. (Ann. Inst. H. Poincaré (B) Probab. Statist. 44 No. 6 (2008), 1038-1077.) arXiv:math/0610645. (Here is the preprint.)
  36. R. Sun and J.M. Swart (2006): The Brownian net. (Ann. Probab. 36 No. 3 (2008), 1153-1208.) arXiv:math.PR/0610625. Here are the third, second, and first version of this preprint, and an addendum to the first version.
  37. J.M. Swart (2006): Duals and thinnings of some relatives of the contact process. (18 pages) arXiv:math.PR/0604335. A shortened version of this preprint has been published as Pages 203-214 in: Prague Stochastics 2006, M. Hušková and M. Janžura (eds.), Matfyzpress, Prague, 2006. This paper has a considerable overlap with M. Hutzenthaler and R. Alkemper: Graphical representation of some duality relations in stochastic population models. (Electron. Commun. Probab. 12 (2007), 206-220).
  38. J.M. Swart (2008): The contact process seen from a typical infected site. (J. Theoret. Probab. 22(3) (2009), 711-740) arXiv:math.PR/0507578v5. Here are the fourth, third, second and first version of this preprint, as well as an addendum to the first version. In the third version, the proof of Prop. 4.4 has been significantly shortened, correcting an error in formula (A.13) of the second version. The first version differs radically from the second and third versions. Chapter 4 of my habilitation thesis is more or less identical to the first version, including the addendum.
  39. K. Fleischmann and J.M. Swart (2005): Renormalization analysis of catalytic Wright-Fisher diffusions. (Electronic J. Probab. 11 (2006) paper no. 24, 585-654) WIAS Preprint No. 1041, (2005) arXiv:math.PR/0506311
  40. S.R. Athreya and J.M. Swart (2004): Branching-coalescing particle systems (Prob. Theory Relat. Fields. 131 No. 3 (2005) 376-414) Theorem 7 in this paper contains an error. Here is a Correction which has also been published on the ArXiv. A note pointing out the error is also published in Prob. Theory Relat. Fields. (Here is the original preprint of the paper.)
  41. J.M. Swart (2003): Uniqueness for isotropic diffusions with a linear drift (Prob. Theory Relat. Fields 128 (2004) 517-524)
  42. K. Fleischmann and J.M. Swart (2002): Trimmed trees and embedded particle systems (Ann. Probab. 32 No. 3A (2004) 2179-2221) (WIAS Berlin, Preprint No. 793, 2002 arXiv:math.PR/0410113)
  43. K. Fleischmann and J.M. Swart (2002): Extinction versus explosion in a supercritical super-Wright-Fisher diffusion (WIAS Berlin, Preprint No. 752, 2002.) (Published as `Extinction versus exponential growth in a supercritical super-Wright-Fisher diffusion' in Stochastic Processes Appl. 106:1 (2003) 141-165 Article in ScienceDirect)
  44. J.M. Swart (2001): A counterexample concerning pathwise uniqueness of 2-dimensional SDE's (Published as "A 2-Dimensional SDE Whose Solutions are Not Unique" in Electron. Commun. Probab. 6 (2001), paper no. 6, 67-71)
  45. J.M. Swart (2000): Pathwise uniqueness for a SDE with non-Lipschitz coefficients (Stochastic Processes Appl. 98 (2002) 131-149 Article in ScienceDirect) Remark: The results in this paper have been improved by D. DeBlassie in Uniqueness for diffusions degenerating at the boundary of a smooth bounded set Ann. Probab. 32(4) (2004) 3167-3190.
  46. J.M. Swart (2000): Clustering of Linearly Interacting Diffusions and Universality of their Long-Time Limit Distribution (Prob. Theory Relat. Fields 118 (2000) 574-594)
  47. F. den Hollander and J.M. Swart (1998): Renormalization of hierarchically interacting isotropic diffusions (J. Stat. Phys. 93 (1998) 243-291)
  48. J.M. Swart (1996): A conditional product measure theorem. (Stat. Probab. Lett. 28 (1996) 131-135). Note: The results in this paper appear to follow from Theorem 5 in R.M. Shortt: Universally measurable spaces: an invariance theorem and diverse characterizations. Fundam. Math. 121, 169-176 (1984).

Lecture notes

Other stuff


Coauthors

Siva R. Athreya

Kun Chen (At Hefei National Laboratory for Physical Sciences at the Microscale)

Youjin Deng

Don Dawson

Klaus Fleischmann (emeritus, formerly WIAS Berlin )

Marco Formentin

Nic Freeman

Andreas Greven

Frank den Hollander

Yuan Huang (At Hefei National Laboratory for Physical Sciences at the Microscale)

Jesper Lykke Jacobsen

Roman Kotecký

Jan Niklas Latz

Tibor Mach

Vít Peržina

Balázs Ráth

Jesús Salas (At University Carlos III of Madrid)

Emmanuel Schertzer

Alan Sokal

Anja Sturm

Rongfeng Sun

Márton Szőke

Tamás Terpai

Florian Völlering

Karel Vrbenský

Jinjiong Yu

Last update: 18.1.24