## Jason Schweinsberg

I am a Professor in the Department of Mathematics at the University of California at San Diego. Before coming to UC San Diego in the Fall of 2004, I got a Ph.D. in Statistics from the University of California at Berkeley in 2001, and then spent three years as an NSF postdoc in the Department of Mathematics at Cornell University.

I work in probability theory, focusing on mathematical problems that arise from the study of evolving populations. Much of my research has been related to stochastic processes involving coalescence, and recently I have been working towards understanding the genealogy of populations undergoing selection. I have also done some research on loop-erased random walks, branching Brownian motion, interacting particle systems, and cancer models. My research is supported in part by NSF Grant DMS-1707953.

Address: Department of Mathematics, 0112; University of California, San Diego; 9500 Gilman Drive; La Jolla, CA 92093-0112
E-mail: jschweinsberg@ucsd.edu
Office: 6157 Applied Physics and Mathematics

### Teaching

I am teaching Math 11 in the Fall of 2020.

Here is a link to a web page where I have compiled some information on graduate programs, REU programs, and careers in Mathematics, which might be of interest to Mathematics majors at UC San Diego.
Here is a link to some information on graduate probability courses, courtesy of Ruth Williams.

### Publications

1. Prediction intervals for neural networks via nonlinear regression (with Richard De Veaux, Jennifer Schumi, and Lyle Ungar). Technometrics, 40 (1998), 273-282. Paper
2. A necessary and sufficient condition for the Λ-coalescent to come down from infinity. Electron. Comm. Probab., 5 (2000), 1-11. Paper
3. Coalescents with simultaneous multiple collisions. Electron. J. Probab., 5 (2000), 1-50. Paper
4. Applications of the continuous-time ballot theorem to Brownian motion and related processes. Stochastic Process. Appl., 95 (2001), 151-176. Paper
5. An O(n2) bound for the relaxation time of a Markov chain on cladograms. Random Struct. Alg., 20 (2002), 59-70. Paper
6. Conditions for recurrence and transience of a Markov chain on Z+ and estimation of a geometric success probability (with James P. Hobert). Ann. Statist. 30 (2002), 1214-1223. Paper
7. Coalescent processes obtained from supercritical Galton-Watson processes. Stochastic Process. Appl., 106 (2003), 107-139. Paper
8. Self-similar fragmentations and stable subordinators (with Grégory Miermont). Séminaire de Probabilités, XXXVII, Lecture Notes in Math., 1832, pp. 333-359, Springer, Berlin (2003). Paper
9. Stability of the tail Markov chain and the evaluation of improper priors for an exponential rate parameter (with James P. Hobert and Dobrin Marchev). Bernoulli, 10 (2004), 549-564. Paper
10. Approximating selective sweeps (with Richard Durrett). Theor. Popul. Biol. 66 (2004), 129-138. Paper
11. Alpha-stable branching and beta-coalescents (with Matthias Birkner, Jochen Blath, Marcella Capaldo, Alison Etheridge, Martin Möhle, and Anton Wakolbinger). Electron. J. Probab. 10 (2005), 303-325. Paper
12. Improving on bold play when the gambler is restricted. J. Appl. Probab. 42 (2005), 321-333. Paper
13. Random partitions approximating the coalescence of lineages during a selective sweep (with Rick Durrett). Ann. Appl. Probab. 15 (2005), 1591-1651. Paper
14. A coalescent model for the effect of advantageous mutations on the genealogy of a population (with Rick Durrett). Stochastic Process. Appl. 115 (2005), 1628-1657. Paper
15. Power laws for family sizes in a duplication model (with Rick Durrett). Ann. Probab. 33 (2005), 2094-2126. Paper
16. Beta-coalescents and continuous stable random trees (with Julien Berestycki and Nathanaël Berestycki). Ann. Probab. 35 (2007), 1835-1887. Paper
17. Small time behavior of beta coalescents (with Julien Berestycki and Nathanaël Berestycki). Ann. Inst. H. Poincaré Probab. Statist. 44 (2008), 214-238. Paper
18. Spatial and non-spatial stochastic models for immune response (with Rinaldo B. Schinazi). Markov Process. Related Fields 14 (2008), 255-276.
19. A contact process with mutations on a tree (with Thomas M. Liggett and Rinaldo B. Schinazi). Stochastic Process. Appl. 118 (2008), 319-332. Paper
20. Loop-erased random walk on finite graphs and the Rayleigh process. J. Theoret. Probab. 21 (2008), 378-396. Paper
21. Waiting for m mutations. Electron. J. Probab. 13 (2008), 1442-1478. Paper
22. The loop-erased random walk and the uniform spanning tree on the four-dimensional discrete torus. Probab. Theory Related Fields. 144 (2009), 319-370. Paper
23. A waiting time problem arising from the study of multi-stage carcinogenesis (with Rick Durrett and Deena Schmidt). Ann. Appl. Probab. 19 (2009), 676-718. Paper
24. The number of small blocks in exchangeable random partitions. ALEA Lat. Am. J. Probab. Math. Stat. 7 (2010), 217-242. Paper
25. Survival of near-critical branching Brownian motion (with Julien Berestycki and Nathanaël Berestycki). J. Statist. Phys. 143 (2011), 833-854. Paper
26. Consensus in the two-state Axelrod model (with Nicolas Lanchier). Stochastic Process. Appl. 122 (2012), 3701-3717. Paper
27. Dynamics of the evolving Bolthausen-Sznitman coalescent. Electron. J. Probab. 17 (2012), no. 91, 1-50. Paper
28. The genealogy of branching Brownian motion with absorption (with Julien Berestycki and Nathanaël Berestycki). Ann. Probab. 41 (2013), 527-618. Paper
29. The evolving beta coalescent (with Götz Kersting and Anton Wakolbinger). Electron. J. Probab. 19 (2014), no. 64, 1-27. Paper
30. Critical branching Brownian motion with absorption: survival probability (with Julien Berestycki and Nathanaël Berestycki). Probab. Theory Related Fields 160 (2014), 489-520. Paper
31. Critical branching Brownian motion with absorption: particle configurations (with Julien Berestycki and Nathanaël Berestycki). Ann. Inst. H. Poincaré Probab. Statist. 51 (2015), 1215-1250. Paper
32. Rigorous results for a population model with selection I: evolution of the fitness distribution. Electron. J. Probab. 22 (2017), no. 37, 1-94. Paper
33. Rigorous results for a population model with selection II: genealogy of the population. Electron. J. Probab. 22 (2017), no. 38, 1-54. Paper
34. A phase transition in excursions from infinity of the "fast" fragmentation-coalescence process (with Andreas Kyprianou, Steven Pagett, and Tim Rogers). Ann. Probab. 45 (2017), 3829-3849. Paper
35. The size of the last merger and time reversal in Λ-coalescents (with Götz Kersting and Anton Wakolbinger). Ann. Inst. H. Poincaré Probab. Statist. 54 (2018), 1527-1555. Paper
36. The nested Kingman coalescent: speed of coming down from infinity (with Airam Blancas, Tim Rogers, and Arno Siri-Jégousse). Ann. Appl. Probab. 29 (2019), 1808-1836. Paper
37. Mutation timing in a spatial model of evolution (with Jasmine Foo and Kevin Leder). Stochastic Process. Appl. 130 (2020), 6388-6413. Paper

### Preprints

1. A Gaussian particle distribution for branching Brownian motion with an inhomogeneous branching rate (with Matthew Roberts). Paper
2. Λ-coalescents arising in populations with dormancy (with Fernando Cordero, Adrián González Casanova, and Maite Wilke-Berenguer). Paper
3. Yaglom-type limit theorems for branching Brownian motion with absorption (with Pascal Maillard). Paper

### Slides for Talks

• "A coalescent model for the effect of advantageous mutations on the genealogy of a population", Paris, September 2007. Slides
• "The loop-erased random walk and the uniform spanning tree on the four-dimensional discrete torus", San Diego, January 2008. Slides
• "A waiting time problem arising from the study of multi-stage carcinogenesis", Beijing, June 2009. Slides
• "The genealogy of branching Brownian motion with absorption", Paris, December 2009. Slides
• "Modeling the genealogy of populations using coalescents with multiple mergers", Singapore, March 2011. Slides
• "Dynamics of the evolving Bolthausen-Sznitman coalescent", Mathematical Biosciences Institute, September 2011. Slides Video
• "Mathematical population genetics and coalescent theory" (series of four 90-minute lectures), Indian Institute of Science, Bangalore, January 2013. Slides
• "Rigorous results for a population model with selection", Isaac Newton Institute, Cambridge, March 2015. Slides Video
• "The nested Kingman coalescent: speed of coming down from infinity", IMS Annual Meeting, Vilnius, Lithuania, July 2018. Slides
• "Yaglom-type limit theorems for branching Brownian motion with absorption", Isaac Newton Institute, Cambridge, July 2018. Slides Video
• "A Gaussian particle distribution for branching Brownian motion with an inhomogeneous branching rate", One World Probability Seminar, May 2020. Slides Video