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作者：Menz, Georg; Otto, Felix
作者单位：Max Planck Society
摘要：We consider a noninteracting unbounded spin system with conservation of the mean spin. We derive a uniform logarithmic Sobolev inequality (LSI) provided the single-site potential is a bounded perturbation of a strictly convex function. The scaling of the LSI constant is optimal in the system size. The argument adapts the two-scale approach of Grunewald, Villani, Westdickenberg and the second author from the quadratic to the general case. Using an asymmetric Brascamp Lieb-type inequality for co...
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作者：Deligiannidis, George; Utev, Sergey
作者单位：University of Oxford; University of Nottingham
摘要：Let X-1, X-2, ... be a centred sequence of weakly stationary random variables with spectral measure F and partial sums S-n = X-1 + ... + X-n. We show that var(S-n) is regularly varying of index gamma at infinity, if and only if G(x) := integral(x)(-x) F(dx) is regularly varying of index 2 - gamma at the origin (0 < gamma < 2).
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作者：Grimmett, Geoffrey R.; Manolescu, Joan
作者单位：University of Cambridge
摘要：All (in)homogeneous bond percolation models on the square, triangular, and hexagonal lattices belong to the same universality class, in the sense that they have identical critical exponents at the critical point (assuming the exponents exist). This is proved using the star triangle transformation and the box-crossing property. The exponents in question are the one-arm exponent rho, the 2j-alternating-arms exponents rho(2j) for j >= 1, the volume exponent delta, and the connectivity exponent et...
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作者：Aidekon, Elie
作者单位：Eindhoven University of Technology
摘要：We consider the minimum of a super-critical branching random walk. Addario-Berry and Reed [Ann. Probab. 37 (2009) 1041-1079] proved the tightness of the minimum centered around its mean value. We show that a convergence in law holds, giving the analog of a well-known result of Bramson [Mem. Amer Math. Soc. 44 (1983) iv+190] in the case of the branching Brownian motion.
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作者：Brzezniak, Zdzislaw; Ondrejat, Martin
作者单位：University of York - UK; Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences
摘要：Let M be a compact Riemannian homogeneous space (e.g., a Euclidean sphere). We prove existence of a global weak solution of the stochastic wave equation D-t partial derivative(t)u = Sigma(d)(k=1) D-xk partial derivative(xk)u+f(u)(Du)+g(u)(D-u)(W) over dot in any dimension d >= 1, where f and g are continuous multilinear maps, and W is a spatially homogeneous Wiener process on R-d with finite spectral measure. A nonstandard method of constructing weak solutions of SPDEs, that does not rely on m...
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作者：Corwin, Ivan; Quastel, Jeremy
作者单位：New York University; University of Toronto
摘要：We consider the weakly asymmetric limit of simple exclusion process with drift to the left, starting from step Bernoulli initial data with rho(-) < rho(+) so that macroscopically one has a rarefaction fan. We study the fluctuations of the process observed along slopes in the fan, which are given by the Hopf-Cole solution of the Kardar-Parisi-Zhang (KPZ) equation, with appropriate initial data. For slopes strictly inside the fan, the initial data is a Dirac delta function and the one point dist...
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作者：Mora, Carlos M.
作者单位：Universidad de Concepcion
摘要：Applying probabilistic techniques we study regularity properties of quantum master equations (QMEs) in the Lindblad form with unbounded coefficients; a density operator is regular if, roughly speaking, it describes a quantum state with finite energy. Using the linear stochastic Schrodinger equation we deduce that solutions of QMEs preserve the regularity of the initial states under a general nonexplosion condition. To this end, we develop the probabilistic representation of QMEs, and we prove ...
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作者：Chen, Louis H. Y.; Fang, Xiao; Shao, Qi-Man
作者单位：National University of Singapore; National University of Singapore; Hong Kong University of Science & Technology; Chinese University of Hong Kong
摘要：Stein's method is applied to obtain a general Cramer-type moderate deviation result for dependent random variables whose dependence is defined in terms of a Stein identity. A corollary for zero-bias coupling is deduced. The result is also applied to a combinatorial central limit theorem, a general system of binary codes, the anti-voter model on a complete graph, and the Curie-Weiss model. A general moderate deviation result for independent random variables is also proved.
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作者：Gurel-Gurevich, Ori; Nachmias, Asaf
作者单位：University of British Columbia
摘要：We show that the distribution of the first return time tau to the origin, v, of a simple random walk on an infinite recurrent graph is heavy tailed and nonconcentrated. More precisely, if d(v) is the degree of v, then for any t >= 1 we have P-v(tau >= t) >= c/d(v)root t and P-v(tau = t vertical bar tau >= t) <= C log(d(v)t)/t for some universal constants c > 0 and C < infinity. The first bound is attained for all t when the underlying graph is Z, and as for the second bound, we construct an ex...
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作者：Marcus, Michael B.; Rosen, Jay
作者单位：City University of New York (CUNY) System; City College of New York (CUNY); City University of New York (CUNY) System; College of Staten Island (CUNY)
摘要：We provide a sufficient condition for the continuity of real valued permanental processes. When applied to the subclass of permanental processes which consists of squares of Gaussian processes, we obtain the sufficient condition for continuity which is also known to be necessary. Using an isomorphism theorem of Eisenbaum and Kaspi which relates Markov local times and permanental processes, we obtain a general sufficient condition for the joint continuity of local times.
