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We study log-correlated Gibbs measures on the $d$-dimensional torus with weakly interacting focusing quartic potentials whose coupling constants tend to $0$ as we remove regularization. In particular, we exhibit a phase transition for this model by i
Externí odkaz:
http://arxiv.org/abs/2412.09790
Autor:
Guan, Qingyang
This note is to study Bourgain's slicing problem following the routes investigated in the last decade. We show that the slicing constant $L_n$ is bounded by $C\log(\log n) $, $n\geq 3$, for some universal constant $C$.
Comment: 21 pages
Comment: 21 pages
Externí odkaz:
http://arxiv.org/abs/2412.09075
Autor:
Zlotchevski, Andrei, Chen, Linan
The Schr\"odinger bridge problem (SBP) seeks to find the measure $\hat{\mathbf{P}}$ on a certain path space which interpolates between state-space distributions $\rho_0$ at time $0$ and $\rho_T$ at time $T$ while minimizing the KL divergence (relativ
Externí odkaz:
http://arxiv.org/abs/2411.13765
Autor:
Li, Xiangting, Chou, Tom
By decoupling forward and backward stochastic trajectories, we develop a family of martingales and work theorems for the same stochastic process. We achieve this by introducing an alternative work theorem derivation that uses tools from stochastic ca
Externí odkaz:
http://arxiv.org/abs/2411.08311
Autor:
Wang, Feng-Yu, Cheng, Li-Juan
By using stochastic analysis, two probability versions of Li-Yau type inequalities are established for diffusion semigroups on a manifold possibly with (non-convex) boundary. The inequalities are explicitly given by the Bakry-Emery curvature-dimensio
Externí odkaz:
http://arxiv.org/abs/2411.03712
A yet unmet challenge in algorithmic fairness is the problem of intersectionality, that is, achieving fairness across the intersection of multiple groups -- and verifying that such fairness has been attained. Because intersectional groups tend to be
Externí odkaz:
http://arxiv.org/abs/2411.02569
In this paper, we establish the existence and uniqueness of solutions of elliptic-parabolic stochastic Keller-Segel systems. The solution is obtained through a carefully designed localization procedure together with some a priori estimates. Both nois
Externí odkaz:
http://arxiv.org/abs/2411.01847
This paper investigates, via methods from the theory of probability on trees, critical phenomena in stochastic cascade models of Yule type, and applies these methods to the problem of uniqueness and nonuniqueness of solutions of particular mean flow
Externí odkaz:
http://arxiv.org/abs/2411.00629
The time evolution of moderately dense gas evolving in vacuum described by the Boltzmann-Enskog equation is studied. The associated stochastic process, the Boltzmann-Enskog process, was constructed by Albeverio, R\"udiger and Sundar (2017) and furthe
Externí odkaz:
http://arxiv.org/abs/2410.21528
Autor:
Jenkins, Paul A.
The Wright-Fisher diffusion is a fundamentally important model of evolution encompassing genetic drift, mutation, and natural selection. Suppose you want to infer the parameters associated with these processes from an observed sample path. Then to wr
Externí odkaz:
http://arxiv.org/abs/2410.15955