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pro vyhledávání: '"82c22"'
We study the space-time scaling limits of solitons in the box-ball system with random initial distribution. In particular, we show that any recentered tagged soliton converges to a Brownian motion in the diffusive space-time scale, and also prove the
Externí odkaz:
http://arxiv.org/abs/2411.14818
This paper investigates the long time dynamics of interacting particle systems subject to singular interactions. We consider a microscopic system of $N$ interacting point particles, where the time evolution of the joint distribution $f_N(t)$ is gover
Externí odkaz:
http://arxiv.org/abs/2411.08614
Autor:
Cohen, David W.
A new adaptation of the Wasserstein metric over the space of probability measures is presented, the associated formal Otto calculus developed, and some transport inequalities are proven. An instance of this new metric can be viewed as a curved versio
Externí odkaz:
http://arxiv.org/abs/2411.05696
This work presents a modification of the self-attention dynamics proposed by Geshkovski et al. (arXiv:2312.10794) to better reflect the practically relevant, causally masked attention used in transformer architectures for generative AI. This modifica
Externí odkaz:
http://arxiv.org/abs/2411.04990
Autor:
Lutsko, Christopher, Toth, Balint
Consider the motion of a charged, point particle moving in the complement of a Poisson distribution of hard sphere scatterers in two dimensions under the effect of a fixed magnetic field. Building on, and extending a coupling method established by th
Externí odkaz:
http://arxiv.org/abs/2411.03984
Bak, Tang, and Wiesenfeld introduced self-organized criticality with the example of a growing sandpile that reaches then sustains a critical density. They presented the abelian sandpile as a potential model. About a decade later, Dickman, Mu\~noz, Ve
Externí odkaz:
http://arxiv.org/abs/2411.02541
Autor:
Dimitrov, Evgeni
We investigate a class of line ensembles whose local structure is described by independent geometric random walk bridges, which have been conditioned to interlace with each other. The latter arise naturally in the context Schur processes, including t
Externí odkaz:
http://arxiv.org/abs/2410.23899
Autor:
Gonçalves, P., Salvador, B.
We investigate the two-points correlation function for several boundary-driven interacting particle systems. Our goal is to show that the time evolution of that correlation function is solution to a partial differential equation that can be written i
Externí odkaz:
http://arxiv.org/abs/2410.17926
Autor:
Aveboukh, Yurii, Volkov, Aleksei
The paper is concerned with the development of Lyapunov methods for the analysis of equilibrium stability in a dynamical system on the space of probability measures driven by a non-local continuity equation. We derive sufficient conditions of stabili
Externí odkaz:
http://arxiv.org/abs/2410.08913
Statistical mechanics explains the properties of macroscopic phenomena based on the movements of microscopic particles such as atoms and molecules. Movements of microscopic particles can be represented by large-scale interacting systems. In this arti
Externí odkaz:
http://arxiv.org/abs/2410.06778