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DTSTART;TZID=America/New_York:20221130T150000
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DTSTAMP:20240110T091213Z
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UID:10001186-1669820400-1669824000@cmsa.fas.harvard.edu
SUMMARY:Lipschitz properties of transport maps under a log-Lipschitz condition
DESCRIPTION:Probability Seminar \n\nLocation: Room 109\, Harvard Science Center\, 1 Oxford Street\, Cambridge MA 02138\nSpeaker: Dan Mikulincer (MIT) \n\n\nTitle: Lipschitz properties of transport maps under a log-Lipschitz condition \nAbstract: Consider the problem of realizing a target probability measure as a push forward\, by a transport map\, of a given source measure. Typically one thinks about the target measure as being ‘complicated’ while the source is simpler and often more structured. In such a setting\, for applications\, it is desirable to find Lipschitz transport maps which afford the transfer of analytic properties from the source to the target. The talk will focus on Lipschitz regularity when the target measure satisfies a log-Lipschitz condition. \nI will present a construction of a transport map\, constructed infinitesimally along the Langevin flow\, and explain how to analyze its Lipschitz constant. The analysis of this map leads to several new results which apply both to Euclidean spaces and manifolds\, and which\, at the moment\, seem to be out of reach of the classically studied optimal transport theory. \nJoint work with Max Fathi and Yair Shenfeld.
URL:https://cmsa.fas.harvard.edu/event/probability-113022/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-11.30.22.png
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DTSTART;TZID=America/New_York:20221116T153000
DTEND;TZID=America/New_York:20221116T163000
DTSTAMP:20240110T084219Z
CREATED:20230802T172705Z
LAST-MODIFIED:20240110T084219Z
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SUMMARY:Outlier-Robust Algorithms for Clustering Non-Spherical Mixtures
DESCRIPTION:Probability Seminar \n\nSpeaker: Ainesh Bakshi (MIT) \nTitle: Outlier-Robust Algorithms for Clustering Non-Spherical Mixtures \nAbstract: In this talk\, we describe the first polynomial time algorithm for robustly clustering a mixture of statistically-separated\, high-dimensional Gaussians. Prior to our work this question was open even in the special case of 2 components in the mixture. Our main conceptual contribution is distilling analytic properties of distributions\, namely hyper-contractivity of degree-two polynomials and anti-concentration of linear projections\, which are necessary and sufficient for clustering.
URL:https://cmsa.fas.harvard.edu/event/probability-111622/
LOCATION:Massachusetts
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-11.16.22.png
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DTSTART;TZID=America/New_York:20221109T153000
DTEND;TZID=America/New_York:20221109T163000
DTSTAMP:20240110T075312Z
CREATED:20230802T172421Z
LAST-MODIFIED:20240110T075312Z
UID:10001184-1668007800-1668011400@cmsa.fas.harvard.edu
SUMMARY:Liouville quantum gravity from random matrix dynamics
DESCRIPTION:Probability Seminar \nSpeaker: Hugo Falconet (Courant Institute\, NYU) \nTitle: Liouville quantum gravity from random matrix dynamics \nAbstract: The Liouville quantum gravity measure is a properly renormalized exponential of the 2d GFF. In this talk\, I will explain how it appears as a limit of natural random matrix dynamics: if (U_t) is a Brownian motion on the unitary group at equilibrium\, then the measures $|det(U_t – e^{i theta}|^gamma dt dtheta$ converge to the 2d LQG measure with parameter $gamma$\, in the limit of large dimension. This extends results from Webb\, Nikula and Saksman for fixed time. The proof relies on a new method for Fisher-Hartwig asymptotics of Toeplitz determinants with real symbols\, which extends to multi-time settings. I will explain this method and how to obtain multi-time loop equations by stochastic analysis on Lie groups. \nBased on a joint work with Paul Bourgade. \n 
URL:https://cmsa.fas.harvard.edu/event/probability-11922/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-11.09.22-1.png
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