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This article investigates the behavior of the continuous-time simple random walk on $\mathbb{Z}^d$, $d \geq 3$. We derive an asymptotic lower bound on the principal exponential rate of decay for the probability that the average value over a large box
Externí odkaz:
http://arxiv.org/abs/2312.17074
Autor:
Barral, Julien, Seuret, Stéphane
In this article, starting from a Gibbs capacity, we build a new random capacity by applying two simple operators, the first one introducing some redundancy and the second one performing a random sampling. Depending on the values of the two parameters
Externí odkaz:
http://arxiv.org/abs/2304.11250
Autor:
Aboulalaa, Adnan
The approach developed in the first part of this work, partly based on large deviations, led to the non-existence of interacting scalar fields as strong limits of regularized fields in finite volume and dimensions $d\geq 4$. This second part deals wi
Externí odkaz:
http://arxiv.org/abs/2212.14879
Autor:
Li, Xinyi, Zhuang, Zijie
We investigate random interlacements on $\mathbb{Z}^d$ with $d \geq 3$, and derive the large deviation rate for the probability that the capacity of the interlacement set in a macroscopic box is much smaller than that of the box. As an application, w
Externí odkaz:
http://arxiv.org/abs/2205.13953
Publikováno v:
Prob. Math. Phys. 3 (2022) 381-429
Wigner's jellium is a model for a gas of electrons. The model consists of $N$ unit negatively charged particles lying in a sea of neutralizing homogeneous positive charge spread out according to Lebesgue measure, and interactions are governed by the
Externí odkaz:
http://arxiv.org/abs/2009.14144
Autor:
Yasodharan, Sarath, Sundaresan, Rajesh
This article examines large time behaviour of finite state mean-field interacting particle systems. Our first main result is a sharp estimate (in the exponential scale) on the time required for convergence of the empirical measure process of the $N$-
Externí odkaz:
http://arxiv.org/abs/1909.03805
Autor:
Sznitman, Alain-Sol
Publikováno v:
Ann. Scient. \'Ec. Norm. Sup., s\'erie 4, t. 56, 801-858, 2023
We investigate certain large deviation asymptotics concerning random interlacements in Z^d, d bigger or equal to 3. We find the principal exponential rate of decay for the probability that the average value of some suitable non-decreasing local funct
Externí odkaz:
http://arxiv.org/abs/1906.05809
Autor:
Aboulalaa, Adnan
The issue of the existence and possible triviality of the Euclidean quantum scalar field in dimension 4 is investigated by using some large deviations techniques. As usual, the field $\varphi_{d}^{4}$ is obtained as a limit of regularized fields $\va
Externí odkaz:
http://arxiv.org/abs/1903.09621
Autor:
Collet, Francesca, Kraaij, Richard C.
Publikováno v:
Stochastic Processes and their Applications Volume 130, Issue 7, July 2020, Pages 4028-4061
We modify the Glauber dynamics of the Curie-Weiss model with dissipation in Dai Pra, Fischer, Regoli[2013] by considering arbitrary transition rates and we analyze the phase-portrait as well as the dynamics of moderate fluctuations for macroscopic ob
Externí odkaz:
http://arxiv.org/abs/1810.10888
A polymer-chain network is a collection of interconnected polymer-chains, made themselves of the repetition of a single pattern called a monomer. Our first main result establishes that, for a class of models for polymer-chain networks, the thermodyna
Externí odkaz:
http://arxiv.org/abs/1809.00598