5期

最新文章

• Bulk diffusion in a system with site disorder AI翻译
  作者：Quastel, Jeremy
  作者单位：University of Toronto
  摘要：We consider a system of random walks in a random environment interacting via exclusion. The model is reversible with respect to a family of disordered Bernoulli measures. Assuming some weak mixing conditions, it is shown that, under diffusive scaling, the system has a deterministic hydrodynamic limit which holds for almost every realization of the environment. The limit is a nonlinear diffusion equation with diffusion coefficient given by a variational formula. The model is nongradient and the...
• Poincare and transportation inequalities for Gibbs measures under the Dobrushin uniqueness condition AI翻译
  作者：Wu, Liming
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Clermont Auvergne (UCA); Wuhan University
  摘要：In in this paper we establish an explicit and sharp estimate of the spectral gap (Poincare inequality) and the transportation inequality for Gibbs measures, under the Dobrushin uniqueness condition. Moreover, we give a generalization of the Liggett's M - epsilon theorem for interacting particle systems.
• A theorem on majorizing measures AI翻译
  作者：Bednorz, Witold
  作者单位：University of Warsaw
  摘要：Let (T,d) be a metric space and phi:R+ -> R an increasing, convex function with phi(0) = 0. We prove that if m is a probability measure m on T which is majorizing with respect to d, phi, that is, delta := sup(x epsilon T)integral(D(T))(0)phi(-1)(1/m(B(x, epsilon))) d epsilon < infinity, then E sup(s,t epsilon T)vertical bar X(s)-X(t)vertical bar <= 32 delta for each separable stochastic process X(t), t epsilon T, which satisfies E phi vertical bar X(s) - X(t)vertical bar/d(s,t) <= 1 for all s,...
• Spectral gap for the zero range process with constant rate AI翻译
  作者：Morris, Ben
  作者单位：University of California System; University of California Davis
  摘要：We solve an open problem concerning the relaxation time (inverse spectral gap) of the zero range process in Z(d)/LZ(d) with constant rate, proving a tight upper bound of 0 ((p + 1)(2)L(2)), where p is the density of particles.
• Threshold for monotone symmetric properties through a logarithmic Sobolev inequality AI翻译
  作者：Rossignol, Raphael
  作者单位：Universite Paris Cite
  摘要：Threshold phenomena are investigated using a general approach, following Talagrand [Ann. Probab. 22 (1994) 1576-1587] and Friedgut and Kalai [Proc. Amer. Math. Soc. 12 (1999) 1017-1054]. The general upper bound for the threshold width of symmetric monotone properties is improved. This follows from a new lower bound on the maximal influence of a variable on a Boolean function. The method of proof is based on a well-know n logarithmic Sobolev inequality on {0, 1}(n). This new bound is shown to b...
• Directed polymers in random environment are diffusive at weak disorder AI翻译
  作者：Comets, Francis; Yoshida, Nobuo
  作者单位：Universite Paris Cite; Kyoto University
  摘要：In this paper we consider directed polymers in random environment with discrete space and time. For transverse dimension at least equal to 3, we prove that diffusivity holds for the path in the full weak disorder region, that is, where the partition function differs from its annealed value only by a non-vanishing factor. Deep inside this region, we also show that the quenched averaged energy has fluctuations of order 1. In complete generality (arbitrary dimension and temperature), we prove mon...