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作者：Sandier, Etienne; Serfaty, Sylvia
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); New York University
摘要：We study the statistical mechanics of classical two-dimensional Coulomb gases with general potential and arbitrary beta, the inverse of the temperature. Such ensembles also correspond to random matrix models in some particular cases. The formal limit case beta = infinity corresponds to weighted Fekete sets and also falls within our analysis. It is known that in such a system points should be asymptotically distributed according to a macroscopic equilibrium measure, and that a large deviations ...
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作者：Tao, Terence; Vu, Van
作者单位：University of California System; University of California Los Angeles; Yale University
摘要：It is a classical result of Ginibre that the normalized bulk k-point correlation functions of a complex n x n Gaussian matrix with independent entries of mean zero and unit variance are asymptotically given by the determinantal point process on C with kernel K-infinity (z, w):=1/pi e-vertical bar z vertical bar(2)/2-vertical bar w vertical bar(2)/2+z (w) over bar in the limit n ->infinity. In this paper, we show that this asymptotic law is universal among all random n x n matrices M-n whose en...
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作者：Gois, B.; Landim, C.
作者单位：Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider the Kawasaki dynamics at inverse temperature beta for the Ising lattice gas on a two-dimensional square of length 2L + 1 with periodic boundary conditions. We assume that initially the particles form a square of length n, which may increase, as well as L, with beta. We show that in a proper time scale the particles form almost always a square and that the center of mass of the square evolves as a Brownian motion when the temperature vanishes.
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作者：Sasada, Makiko
作者单位：Keio University
摘要：We give a lower bound on the spectral gap for a class of stochastic energy exchange models. In 2011, Grigo et al. introduced the model and showed that, for a class of stochastic energy exchange models with a uniformly positive rate function, the spectral gap of an N-component system is bounded from below by a function of order N-2. In this paper, we consider the case where the rate function is not uniformly positive. For this case, the spectral gap depends not only on N but also on the average...
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作者：Freeman, Nic
作者单位：University of Oxford
摘要：We construct an extension of the A-coalescent to a spatial continuum and analyse its behaviour. Like the A-coalescent, the individuals in our model can be separated into (i) a dust component and (ii) large blocks of coalesced individuals. We identify a five phase system, where our phases are defined according to changes in the qualitative behaviour of the dust and large blocks. We completely classify the phase behaviour, including necessary and sufficient conditions for the model to come down ...
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作者：Harangi, Viktor; Virag, Balint
作者单位：University of Toronto
摘要：A theorem of Hoffman gives an upper bound on the independence ratio of regular graphs in terms of the minimum lambda(min) of the spectrum of the adjacency matrix. To complement this result we use random eigenvectors to gain lower bounds in the vertex-transitive case. For example, we prove that the independence ratio of a 3-regular transitive graph is at least q = 1/2 - 3/4 pi arccos (1-lambda(min)/4). The same bound holds for infinite transitive graphs: we construct factor of i.i.d. independen...
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作者：Lyons, Terry; Ni, Hao
作者单位：University of Oxford
摘要：The signature of a path provides a top down description of the path in terms of its effects as a control [Differential Equations Driven by Rough Paths (2007) Springer]. The signature transforms a path into a group-like element in the tensor algebra and is an essential object in rough path theory. The expected signature of a stochastic process plays a similar role to that played by the characteristic function of a random variable. In [Chevyrev (2013)], it is proved that under certain boundednes...
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作者：Brofferio, Sara; Buraczewski, Dariusz
作者单位：Universite Paris Saclay; Universite Paris Saclay; University of Wroclaw
摘要：We consider stochastic dynamical systems on R, that is, random processes defined by X-n(x) = Psi(n)(X-n-1(x)), X-0(x) = x, where Psi(n) are i.i.d. random continuous transformations of some unbounded closed subset of R. We assume here that Psi(n) behaves asymptotically like A(n)x, for some random positive number A(n) [the main example is the affine stochastic recursion Psi(n) (x) = A(n)x + B-n]. Our aim is to describe invariant Radon measures of the process X-n(x) in the critical case, when E l...
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作者：Dupuis, Paul; Liu, Yufei
作者单位：Brown University; Alphabet Inc.; Google Incorporated
摘要：The large deviations principle for the empirical measure for both continuous and discrete time Markov processes is well known. Various expressions are available for the rate function, but these expressions are usually as the solution to a variational problem, and in this sense not explicit. An interesting class of continuous time, reversible processes was identified in the original work of Donsker and Varadhan for which an explicit expression is possible. While this class includes many (revers...
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作者：Camia, Federico; Garban, Christophe; Newman, Charles M.
作者单位：Vrije Universiteit Amsterdam; New York University; New York University Abu Dhabi; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON); New York University; Vrije Universiteit Amsterdam; University of California System; University of California Irvine
摘要：The aim of this paper is to prove the following result. Consider the critical Ising model on the resealed grid aZ(2), then the renormalized magnetization field Phi(a) := a(15/8)s Sigma(x is an element of aZ2)sigma(x)delta(x), seen as a random distribution (i.e., generalized function) on the plane, has a unique scaling limit as the mesh size a SE arrow 0. The limiting field is conformally covariant.
