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 280A in the Fall 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
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Prediction intervals for neural networks via nonlinear regression
(with Richard De Veaux, Jennifer Schumi, and Lyle Ungar).
Technometrics, 40 (1998), 273-282.
Paper
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A necessary and sufficient condition for the Λ-coalescent to
come down from infinity.
Electron. Comm. Probab., 5 (2000), 1-11.
Paper
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Coalescents with simultaneous multiple collisions.
Electron. J. Probab., 5 (2000), 1-50.
Paper
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Applications of the continuous-time ballot theorem to Brownian motion
and related processes.
Stochastic Process. Appl., 95 (2001), 151-176.
Paper
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An O(n2) bound for the relaxation time of a Markov chain on cladograms.
Random Struct. Alg., 20 (2002), 59-70.
Paper
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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
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Coalescent processes obtained from supercritical Galton-Watson processes.
Stochastic Process. Appl., 106 (2003), 107-139.
Paper
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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
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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
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Approximating selective sweeps (with Richard Durrett).
Theor. Popul. Biol. 66 (2004), 129-138.
Paper
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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
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Improving on bold play when the gambler is restricted.
J. Appl. Probab. 42 (2005), 321-333.
Paper
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Random partitions approximating the coalescence of lineages during
a selective sweep (with Rick Durrett).
Ann. Appl. Probab. 15 (2005), 1591-1651.
Paper
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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
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Power laws for family sizes in a duplication model (with Rick Durrett).
Ann. Probab. 33 (2005), 2094-2126.
Paper
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Beta-coalescents and continuous stable random trees (with Julien Berestycki and Nathanaël Berestycki). Ann. Probab. 35 (2007), 1835-1887.
Paper
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Small time behavior of beta coalescents (with Julien Berestycki and Nathanaël Berestycki). Ann. Inst. H. Poincaré Probab. Statist. 44 (2008), 214-238.
Paper
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Spatial and non-spatial stochastic models for immune response (with Rinaldo B. Schinazi). Markov Process. Related Fields 14 (2008), 255-276.
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A contact process with mutations on a tree (with Thomas M. Liggett
and Rinaldo B. Schinazi). Stochastic Process. Appl. 118 (2008), 319-332.
Paper
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Loop-erased random walk on finite graphs and the Rayleigh process. J. Theoret. Probab. 21 (2008), 378-396.
Paper
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Waiting for m mutations. Electron. J. Probab. 13 (2008), 1442-1478.
Paper
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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
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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
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The number of small blocks in exchangeable random partitions. ALEA Lat. Am. J. Probab. Math. Stat. 7 (2010), 217-242.
Paper
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Survival of near-critical branching Brownian motion (with Julien Berestycki and Nathanaël Berestycki). J. Statist. Phys. 143 (2011), 833-854.
Paper
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Consensus in the two-state Axelrod model (with Nicolas Lanchier). Stochastic Process. Appl. 122 (2012), 3701-3717.
Paper
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Dynamics of the evolving Bolthausen-Sznitman coalescent. Electron. J. Probab. 17 (2012), no. 91, 1-50.
Paper
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The genealogy of branching Brownian motion with absorption (with Julien Berestycki and Nathanaël Berestycki). Ann. Probab. 41 (2013), 527-618.
Paper
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The evolving beta coalescent (with Götz Kersting and Anton Wakolbinger). Electron. J. Probab. 19 (2014), no. 64, 1-27.
Paper
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Critical branching Brownian motion with absorption: survival probability (with Julien Berestycki and Nathanaël Berestycki). Probab. Theory Related Fields 160 (2014), 489-520.
Paper
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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
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Rigorous results for a population model with selection I: evolution of the fitness distribution. Electron. J. Probab. 22 (2017), no. 37, 1-94.
Paper
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Rigorous results for a population model with selection II: genealogy of the population. Electron. J. Probab. 22 (2017), no. 38, 1-54.
Paper
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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
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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
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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
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Mutation timing in a spatial model of evolution (with Jasmine Foo and Kevin Leder).
Stochastic Process. Appl. 130 (2020), 6388-6413.
Paper
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A Gaussian particle distribution for branching Brownian motion with an inhomogeneous branching rate (with Matthew Roberts).
Electron. J. Probab. 26 (2021), 1-76.
Paper
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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
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Yaglom-type limit theorems for branching Brownian motion with absorption (with Pascal Maillard). Annales Henri Lebesgue 5 (2022), 921-985.
Paper
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Particle configurations for branching Brownian motion with an inhomogeneous branching rate (with Jiaqi Liu). ALEA Lat. Am. J. Probab. Math. Stat. 20 (2023), 731-803.
Paper
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cloneRate: fast estimation of single-cell clonal dynamics using coalescent theory (with Brian Johnson, Yubo Shuai, and Kit Curtius). Bioinformatics (2023).
Paper
Preprints
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A spatial mutation model with increasing mutation rates (with Brian Chao). To appear in J. Appl. Probab. Paper
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Asymptotics for the site frequency spectrum associated with the genealogy of a birth and death process (with Yubo Shuai). Paper
Slides for Talks
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"A coalescent model for the effect of advantageous mutations on the genealogy of a population", Paris, September 2007.
Slides
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"The loop-erased random walk and the uniform spanning tree on the four-dimensional discrete torus", San Diego, January 2008.
Slides
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"A waiting time problem arising from the study of multi-stage carcinogenesis", Beijing, June 2009.
Slides
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"The genealogy of branching Brownian motion with absorption", Paris, December 2009.
Slides
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"Modeling the genealogy of populations using coalescents with multiple mergers", Singapore, March 2011.
Slides
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"Dynamics of the evolving Bolthausen-Sznitman coalescent", Mathematical Biosciences Institute, September 2011.
Slides
Video
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"Mathematical population genetics and coalescent theory" (series of four 90-minute lectures), Indian Institute of Science, Bangalore, January 2013.
Slides
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"Rigorous results for a population model with selection", Isaac Newton Institute, Cambridge, March 2015.
Slides
Video
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"The nested Kingman coalescent: speed of coming down from infinity", IMS Annual Meeting, Vilnius, Lithuania, July 2018.
Slides
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"Yaglom-type limit theorems for branching Brownian motion with absorption", Isaac Newton Institute, Cambridge, July 2018.
Slides
Video
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"A Gaussian particle distribution for branching Brownian motion with an inhomogeneous branching rate", One World Probability Seminar, May 2020.
Slides
Video
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"Modeling the evolution of populations undergoing selection using branching Brownian motion" (series of five 60-minute lectures), Centre de Recherches Mathématiques, Montreal, May 2022.
Slides
Video 1
Video 2
Video 3
Video 4
Video 5
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"Λ-coalescents arising in a population with dormancy", Hausdorff Institute, Bonn, June 2022.
Slides
Video
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"Asymptotics for the site frequency spectrum associated with the genealogy of a birth and death process", Toulouse, May 2023.
Slides