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作者：Gentil, I; Guillin, A; Miclo, L
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：We present a class of modified logarithmic Sobolev inequality, interpolating between Poincare and logarithmic Sobolev inequalities, suitable for measures of the type exp(-| x|(alpha)) or exp(-| x|(alpha) log(beta) ( 2 + | x|)) (alpha is an element of] 1, 2[ and beta is an element of R) which lead to new concentration inequalities. These modified inequalities share common properties with usual logarithmic Sobolev inequalities, as tensorisation or perturbation, and imply as well Poincare inequal...
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作者：Zerner, MPW
作者单位：Eberhard Karls University of Tubingen
摘要：We introduce a class of nearest-neighbor integer random walks in random and non-random media, which includes excited random walks considered in the literature. At each site the random walker has a drift to the right, the strength of which depends on the environment at that site and on how often the walker has visited that site before. We give exact criteria for recurrence and transience and consider the speed of the walk.
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作者：Petz, D; Réffy, J
作者单位：Budapest University of Technology & Economics
摘要：Let U-m be an mxm Haar unitary matrix and U-[m,U-n] be its nxn truncation. In this paper the large deviation is proven for the empirical eigenvalue density of U-[m,U-n] as m/n -> lambda and n -> infinity. The rate function and the limit distribution are given explicitly. U-[m,U-n] is the random matrix model of quq, where u is a Haar unitary in a finite von Neumann algebra, q is a certain projection and they are free. The limit distribution coincides with the Brown measure of the operator quq.
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作者：Giacomin, G; Toninelli, FL
作者单位：Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Ecole Normale Superieure de Lyon (ENS de LYON)
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作者：Collins, B
作者单位：Kyoto University
摘要：We consider the product of two independent randomly rotated projectors. The square of its radial part turns out to be distributed as a Jacobi ensemble. We study its global and local properties in the large dimension scaling relevant to free probability theory. We establish asymptotics for one point and two point correlation functions, as well as properties of largest and smallest eigenvalues.
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作者：Feldman, GM
作者单位：National Academy of Sciences Ukraine; B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine
摘要：The well-known Skitovich-Darmois theorem asserts that a Gaussian distribution is characterized by the independence of two linear forms of independent random variables. The similar result was proved by Heyde, where instead of the independence, the symmetry of the conditional distribution of one linear form given another was considered. In this article we prove that the Heyde theorem on a locally compact Abelian group X remains true if and only if X contains no elements of order two. We describe...
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作者：Fang, SZ; Zhang, TS
作者单位：Universite Bourgogne Europe; University of Manchester
摘要：We study a class of stochastic differential equations with non-Lipschitz coefficients. A unique strong solution is obtained and the non confluence of the solutions of stochastic differential equations is proved. The dependence with respect to the initial values is investigated. To obtain a continuous version of solutions, the modulus of continuity of coefficients is assumed to be less than |x-y| log 1/vertical bar x-y vertical bar. Finally a large deviation principle of Freidlin-Wentzell type ...
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作者：Blath, J; Mörters, P
作者单位：University of Oxford; University of Bath
摘要：We determine for a super-Brownian motion {X-t : t >= 0} in R-d, d >= 3, the precise gauge function phi such that, almost surely on survival up to time t, [GRAPHICS] improving a result of Barlow, Evans and Perkins about the most visited sites of super-Brownian motion. We also determine upper and lower bounds for the Hausdorff dimension spectrum of thick points refining the multifractal analysis of super-Brownian motion by Taylor and Perkins. The upper bound, conjectured to be sharp, involves a ...
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作者：Gurevich, BM; Tempelman, AA
作者单位：Lomonosov Moscow State University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：We refine some well-known approximation theorems in the theory of homogeneous lattice random fields. In particular, we prove that every translation invariant Borel probability measure mu on the space X of finite-alphabet configurations on Z(d), d >= 1, can be weakly approximated by Markov measures mu(n) with supp(mu(n)) = X and with the entropies h(mu(n)) --> h(mu). The proof is based on some facts of Thermodynamic Formalism; we also present an elementary constructive proof of a weaker version...
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作者：Graham, C
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We consider N single server infinite buffer queues with service rate beta. Customers arrive at rate Nalpha, choose L queues uniformly, and join the shortest. We study the processes t is an element of R+ (bar right arrow) R-t(N) = (R-t(N)(k))(kis an element ofN) for large N, where R-t(N)(k) is the fraction of queues of length at least k at time t. Laws of large numbers (LLNs) are known, see Vvedenskaya et al. [15], Mitzenmacher [12] and Graham [5]. We consider certain Hilbert spaces with the we...
