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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：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：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：Berti, Patrizia; Pratelli, Luca; Rigo, Pietro
作者单位：Universita di Modena e Reggio Emilia; University of Pavia
摘要：Let S be a Polish space and (X-n : n >= 1) an exchangeable sequence of S-valued random variables. Let alpha(n)(.) = P(Xn+1 is an element of E . vertical bar X-1, ... X-n) be the preweak dictive measure and a a random probability measure on S such that an alpha(n) -> weak alpha a.s. Two (related) problems are addressed. One is to give conditions for alpha << lambda a.s., where lambda is a (nonrandom) sigma-finite Borel measure on S. Such conditions should concern the finite dimensional distribu...
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作者：Rezakhanlou, Fraydoun
作者单位：University of California System; University of California Berkeley
摘要：The Marcus-Lushnikov process is a simple mean field model of coagulating particles that converges to the homogeneous Smoluchowski equation in the large mass limit. If the coagulation rates grow sufficiently fast as the size of particles get large, giant particles emerge in finite time. This is known as gelation, and such particles are known as gels. Gelation comes in different flavors: simple, instantaneous and complete. In the case of an instantaneous gelation, giant particles are formed in a...
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作者：Deroin, B.; Kleptsyn, V.; Navas, A.; Parwani, K.
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rennes; Universidad de Santiago de Chile; Eastern Illinois University
摘要：We study symmetric random walks on finitely generated groups of orientation-preserving homeomorphisms of the real line. We establish an oscillation property for the induced Markov chain on the line that implies a weak form of recurrence. Except for a few special cases, which can be treated separately, we prove a property of global stability at a finite distance: roughly speaking, there exists a compact interval such that any two trajectories get closer and closer whenever one of them returns t...
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作者：Erdos, Laszlo; Knowles, Antti; Yau, Horng-Tzer; Yin, Jun
作者单位：University of Munich; Harvard University; University of Wisconsin System; University of Wisconsin Madison
摘要：We consider the ensemble of adjacency matrices of Erdos-Renyi random graphs, that is, graphs on N vertices where every edge is chosen independently and with probability p equivalent to p(N). We rescale the matrix so that its bulk eigenvalues are of order one. We prove that, as long as pN -> infinity (with a speed at least logarithmic in N), the density of eigenvalues of the Erdos-Renyi ensemble is given by the Wigner semicircle law for spectral windows of length larger than N-1 (up to logarith...
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作者：Kwasnicki, Mateusz; Malecki, Jacek; Ryznar, Michal
作者单位：Wroclaw University of Science & Technology; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; Universite d'Angers
摘要：In this paper we study the supremum functional M-t = sup(0 <= s <= t) X-s, where X-t, t >= 0, is a one-dimensional Levy process. Under very mild assumptions we provide a simple, uniform estimate of the cumulative distribution function of Mt. In the symmetric case we find an integral representation of the Laplace transform of the distribution of M-t if the Levy-Khintchin exponent of the process increases on (0, infinity).
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作者：Prokaj, Vilmos
作者单位：Eotvos Lorand University
摘要：The Tanaka equation dX(t) = sign(X-t)dB(t) is an example of a stochastic differential equation (SDE) without strong solution. Hence pathwise uniqueness does not hold for this equation. In this note we prove that if we modify the right-hand side of the equation, roughly speaking, with a strong enough additive noise, independent of the Brownian motion B, then the solution of the obtained equation is pathwise unique.
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作者：Cheliotis, Dimitris; Virag, Balint
作者单位：National & Kapodistrian University of Athens; University of Toronto; University of Toronto
摘要：Sinai's random walk in random environment shows interesting patterns on the exponential time scale. We characterize the patterns that appear on infinitely many time scales after appropriate resealing (a functional law of iterated logarithm). The curious rate function captures the difference between one-sided and two-sided behavior.
