Sunday, November 3
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Session Chair: Wei Wu, NYU Shanghai |
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9:00-10:00 AM
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Stochastic description of noisy signals: Different approaches By Roberto Fernandez, NYU Shanghai A discrete noisy signal (binned spike trains, DNA configurations, discretized sound bits) can be modelled by probability measures on AZ, with A (alphabet) a finite set. It is natural to wonder about efficient ways to describe such measures. Several possibilities have been considered by different mathemat-ical areas: Markovian and Non-Markovian processes in probability, Gibbs measures in statistical mechanics, Bowen measures in the theory of dynamical systems, and a few more. The talk will present and compare these different approaches, emphasizing advantages and disadvantages of each of them, and cases of equivalence or lack of equivalence of different treatments. |
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10:00-10:30 AM |
Morning Tea Break |
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10:30-11:30 AM
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Sharp threshold sequence and universality for Ising perceptron models By Shuta Nakajima, Meiji University In this talk, we discuss a family of Ising perceptron models with {0,1}-valued activation functions. This includes the classical half-space models and some of the symmetric models considered in recent works. For each of these models, we show that the free energy is self-averaging, there is a sharp threshold sequence, and the free energy is universal concerning the disorder. A prior work by Xu (2019) used very different methods to show a sharp threshold sequence in the half-space Ising perceptron with Bernoulli disorder. Recent works of Perkins-Xu (2021) and Abbe-Li-Sly (2021) determined the sharp threshold and the limiting free energy in a symmetric perceptron model. The results apply in more general settings and are based on new "add one constraint" estimates extending Talagrand's estimates for the half-space model. This talk is based on joint work with Nike Sun (MIT). |
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11:30 AM-12:30 PM
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Limit Properties of Record Numbers in Random walks By Qiang Yao, East China Normal University We summarize and enhance the understanding of weak convergence and functional limits for record numbers in discrete-time random walks under Spitzer’s condition, and extend these findings to σ-record numbers. Then we identify a sufficient condition for the existence of functional limits for record numbers in continuous-time random walks. Finally, we derive large deviations, moderate deviations, and laws of the iterated logarithm for record numbers in discrete-time random walks. (Joint work with Yuqiang Li and Penghui Lu.) |
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12:30 PM-2:30 PM |
Lunch Break Session |
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Session Chair: Eric Endo, NYU Shanghai |
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2:30-3:30 PM
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Infinite differentiability of the free energy for a Derrida-Retaux system By Xinxing Chen, Shanghai Jiao Tong University We consider a recursive system which was introduced by Derrida and Retaux (2014) as a toy model to study the depinning transition in presence of disorder. Derrida and Retaux predicted the free energy $F_\infty(p)$ of the system exhibit quite an unusual physical phenomenon which is an infinite order phase transition. Hu and Shi (2018) studied a special situation and obtained other behavior of the free energy, while insisted on $p=p_c$ being an essential singularity. Recently, Chen, Dagard, Derrida, Hu, Lifshits and Shi (2021) confirmed the Derrida-Retaux conjecture under suitable integrability condition. However, from a mathematical point of view, it is still unknown whether the free energy is infinitely differentiable at the critical point. So that, we continue to study the infinite differentiability of the free energy in this paper. |
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3:30-4:00 PM |
Afternoon Tea Break |
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4:00-4:40 PM
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Quasi-invariant theorem on general Riemannian loop space By Bo Wu, Fudan University In this talk, we will first introduce gradient and Hessian estimates for logarithmic heat kernel on a general complete Riemannian manifold, by which Quasi-invariant theorem with respect to the Brownian Bridge measure on associated Riemannian loop space will be presented. This talk is based on a joint work with Chen Xin and Xue-Mei Li. |