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作者：Peccati, G
作者单位：Universite Paris Saclay; Bocconi University
摘要：Consider a (possibly infinite) exchangeable sequence X = {X-n : 1 less than or equal to n < N}, where N is an element of N boolean OR {infinity}, with values in a Borel space (A, A), and note X-n = (X-1,..., X-n). We say that X is Hoeffding decomposable if, for each n, every square integrable, centered and symmetric statistic based on Xn can be written as an orthogonal sum of n U-statistics with degenerated and symmetric kernels of increasing order. The only two examples of Hoeffding decomposa...
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作者：Funaki, T
作者单位：University of Tokyo
摘要：We consider a system of interacting Brownian particles in R-d with a pairwise potential, which is radially symmetric, of finite range and attains a unique minimum when the distance of two particles becomes a > 0. The asymptotic behavior of the system is studied under the zero temperature limit from both microscopic and macroscopic aspects. If the system is rigidly crystallized, namely if the particles are rigidly arranged in an equal distance a, the crystallization is kept under the evolution ...
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作者：Iksanov, AM; Jurek, ZJ; Schreiber, BM
作者单位：Ministry of Education & Science of Ukraine; Taras Shevchenko National University of Kyiv; University of Wroclaw
摘要：We prove that the convolution of a selfdecomposable distribution with its background driving law is again selfdecomposable if and only if the background driving law is s-selfdecomposable. We will refer to this as the factorization property of a selfdecomposable distribution; let L-f denote the set of all these distributions. The algebraic structure and various characterizations of L-f are studied. Some examples are discussed, the most interesting one being given by the Levy stochastic area int...
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作者：Le Jan, Y; Raimond, O
作者单位：Universite Paris Saclay
摘要：We are interested in stationary fluid random evolutions with independent increments. Under some mild assumptions, we show they are solutions of a stochastic differential equation (SDE). There are situations where these evolutions are not described by flows of diffeomorphisms, but by coalescing flows or by flows of probability kernels. In an intermediate phase, for which there exist a coalescing flow and a flow of kernels solution of the SDE, a classification is given: All solutions of the SDE ...
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作者：Dolgopyat, D; Kaloshin, V; Koralov, L
作者单位：University System of Maryland; University of Maryland College Park; California Institute of Technology; Princeton University
摘要：We consider a stochastic flow driven by a finite-dimensional Brownian motion. We show that almost every realization of such a flow exhibits strong statistical properties such as the exponential convergence of an initial measure to the equilibrium state and the central limit theorem. The proof uses new estimates of the mixing rates of the multi-point motion.
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作者：Piau, D
作者单位：Universite Claude Bernard Lyon 1
摘要：The immortal branching Markov process (iBMP) is a modification of the usual branching model, in which each particle of generation 17 is counted, in addition to its offspring, as a member of generation n + 1, its state being unchanged. When the number of offspring is Bernoulli, iBMP accounts, for instance, for the variability of the biological sequences that are produced by polymerase chain reactions (PCRs). This variability is due to the mutations and to the incomplete replications that affect...
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作者：Barlow, MT
作者单位：University of British Columbia
摘要：We obtain Gaussian upper and lower bounds on the transition density q(t)(x, y) of the continuous time simple random walk on a supercritical percolation cluster C(infinity) in the Euclidean lattice. The bounds, analogous to Aronsen's bounds for uniformly elliptic divergence form diffusions, hold with constants c(i) depending only on p (the percolation probability) and d. The irregular nature of the medium means that the bound for q(t) (x, (.)) holds only for t greater than or equal to S(x) (ome...
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作者：Luschgy, H; Pagès, G
作者单位：Universitat Trier; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite
摘要：The sharp asymptotics for the L-2-quantization errors of Gaussian measures on a Hilbert space and, in particular, for Gaussian processes is derived. The condition imposed is regular variation of the eigenvalues.
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作者：Lutwak, E; Yang, D; Zhang, GY
作者单位：New York University; New York University Tandon School of Engineering
摘要：It is shown that the product of the Renyi entropies of two independent random vectors provides a sharp lower bound for the expected value of the moments of the inner product of the random vectors. This new inequality contains important geometry (such as extensions of one of the fundamental affine isoperimetric inequalities, the Blaschke-Santalo inequality).
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作者：Chen, X
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：Let alpha([0, 1](P)) denote the intersection local time of p independent d-dimensional Brownian motions running up to the time 1. Under the conditions p(d - 2) < d and d greater than or equal to 2, we prove lim(t-->infinity) t(-1) logP{alpha([0, 1](P)) greater than or equal to t((d(p-1))/2)} = -gammaalpha(d, p) with the right-hand side being identified in terms of the the best constant of the Gagliardo-Nirenberg inequality. Within the scale of moderate deviations, we also establish the precise...
