Probability and Mathematical Physics Seminar
This seminar covers a wide range of topics in pure and applied probability and in mathematical physics. Unless otherwise noted, the talks take place on Fridays, 11:10am–12pm, in room WWH 1302. See directions to the Courant Institute.
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Twice every semester, we will have a joint Columbia–Courant meeting (hosted once at each institution) as the Probability and the City seminar.
Seminar Organizer(s): Eyal Lubetzky, Paul Bourgade, Klara Courteaut, and the probability group
Upcoming Events
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Friday, February 13, 202611:10AM, Warren Weaver Hall 1302
Recent results on polaron path measures
Tobias Schmidt, Technische Universität DarmstadtSynopsis:
Polaron models describe a quantum particle interacting with a bosonic scalar field. They give rise to a Gibbsian reweighting of Brownian motion via Feynman-Kac formulas, where the Gibbs action induces a self-interaction of the path. One of the most famous examples is the Fröhlich polaron. In this talk, we study the long-time diffusive behavior of the path endpoint under such measures. Using correlation inequalities and Gaussian domination techniques, we discuss how the interaction alters the mean-square displacement, both in translation-invariant models and in more general settings. Joint work with Volker Betz (Darmstadt) and Mark Sellke (Harvard).
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Friday, February 20, 202611:10AM, Warren Weaver Hall 1302
TBA
Tyler Helmuth, Durham University
Past Events
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Friday, February 6, 202611:10AM, Warren Weaver Hall 1302
Extremal scaling limits for random walks in space-time random environments
Hindy Drillick, Courant InstituteSynopsis:
In this talk, we will consider random walks in a space-time random environment, which can be thought of as a discrete model for diffusing particles in a time-dependent random medium. We will study the scaling limits of these models in certain moderate deviation scaling regimes and show that they are described by stochastic PDEs. The solutions to these SPDEs are Gaussian processes up to a dimension-dependent critical scale. In d=1 we prove that the critical fluctuations are given by the KPZ equation. In d=2, we conjecture that the scaling limit at criticality is given by the 2d critical stochastic heat flow recently constructed by Caravenna, Sun, and Zygouras. This is based on joint works with Sayan Das and Shalin Parekh.
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Friday, January 30, 202612PM, Warren Weaver Hall 1302
Quantum mixing on large Schreier graphs
Charles Bordenave, CNRS & Institut de Mathématiques de MarseilleSynopsis:
Quantum ergodicity describes the delocalization of most eigenfunctions of Laplace-type operators on graphs or manifolds exhibiting chaotic classical dynamics. Quantum mixing is a stronger notion, additionally controlling correlations between eigenfunctions at different energy levels. In this work, we study families of finite Schreier graphs that converge to an infinite Cayley graph and establish quantum mixing under the assumption that the limiting Cayley graph has absolutely continuous spectrum. The proof relies on a new approach to quantum ergodicity, based on trace computations, resolvent approximations and representation theory. This is a joint work with Cyril Letrouit and Mostafa Sabri.