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.
To be kept informed, you can subscribe to the Probability Seminar Mailing list.
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 14, 202511:10AM, Warren Weaver Hall 1302
Gradient interface models: scaling limits and extrema
Florian Schweiger, University of GenevaSynopsis:
Gradient interface models are lattice models from statistical mechanics that arise when describing the microscopic fluctuations of interfaces in nature. While many of their features are believed to be universal, rigorous results are often known only for specific classes of models. I will survey some of these results, and then describe two recent advances: The behavior of the maximum for two-dimensional fields with strictly convex interaction, and scaling limits of the fields for general monotone interactions with quadratic growth.
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Friday, February 21, 202511:10AM, Warren Weaver Hall 1302
Benjamini-Schramm conjecture and the loop O(n) model
Alexander Glazman, University of InnsbruckSynopsis:
We witness many phase transitions in everyday life (eg. ice melting to water). The mathematical approach to these phenomena revolves around the percolation model: given a graph, call each vertex open with probability p independently of the others and look at the subgraph induced by open vertices. Benjamini and Schramm conjectured in 1996 that, at p=1/2, on any planar graph, either there is no infinite connected components or infinitely many.
We prove a stronger version of this conjecture for virtually all planar graphs. We then use this to establish fractal macroscopic behaviour in the loop O(n) model. The latter includes a random discrete Lipschitz surface as a particular case.
Joint work with Matan Harel and Nathan Zelesko.
Past Events
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Friday, February 7, 202511:10AM, Warren Weaver Hall 1302
Rough calculus
Rama Cont, Oxford UniversitySynopsis:
Rough calculus is a pathwise extension of the Ito calculus to smooth function(al)s of paths and processes with arbitrary Hölder regularity.
We construct integrals of k-jets along irregular paths with finite p-th variation for any p >1, and derive change of variable formulas for smooth functions of such paths. The case p=2 corresponds to Hans Foellmer's pathwise Ito formula while the case p>2 leads to a "higher order Ito calculus".
The framework is entirely pathwise but applicable to stochastic processes with irregular trajectories, such as (fractional) Brownian motions with arbitrary Hurst exponent. As an application, we show how these results lead to new insights on the transport of measures along rough trajectories.