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. I have particularly focused on understanding the evolution of populations undergoing selection, often using models based on branching Brownian motion. I have also done some research on cancer models, loop-erased random walks, and interacting particle systems.

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 180B in the Winter of 2023.

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
  38. A Gaussian particle distribution for branching Brownian motion with an inhomogeneous branching rate (with Matthew Roberts). Electron. J. Probab. 26 (2021), 1-76. Paper
  39. Λ-coalescents arising in a population with dormancy (with Fernando Cordero, Adrián González Casanova, and Maite Wilke-Berenguer). Electron. J. Probab. 27 (2022), 1-34. Paper
  40. Yaglom-type limit theorems for branching Brownian motion with absorption (with Pascal Maillard). Annales Henri Lebesgue 5 (2022), 921-985. Paper

Preprints

  1. A spatial mutation model with increasing mutation rates (with Brian Chao). Paper
  2. Particle configurations for branching Brownian motion with an inhomogeneous branching rate (with Jiaqi Liu). Paper
  3. Estimating single cell clonal dynamics in human blood using coalescent theory (with Brian Johnson, Yubo Shuai, and Kit Curtius). Paper

Slides for Talks