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作者：Bobkov, SG
作者单位：Syktyvkar State University; University System of Georgia; Georgia Institute of Technology
摘要：We discuss an approach, based on the Brunn-Minkowski inequality, to isoperimetric and analytic inequalities for probability measures on Euclidean space with logarithmically concave densities. In particular, we show that such measures have positive isoperimetric constants in the sense of Cheeger and thus always share Poincare-type inequalities. We then describe those log-concave measures which satisfy isoperimetric inequalities of Gaussian type. The results are precised in dimension 1.
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作者：Daley, DJ
作者单位：Australian National University
摘要：A stationary renewal process N(.) for which the lifetime distribution has its hth moment finite or infinite according as k is less than or greater than kappa for some 1 < K < 2, is long-range dependent and has Hurst index alpha = (1/2)(3-kappa) (this is the critical index alpha for which lim sup(t-->infinity) t(-2a) var N(0, t] is finite or infinite according as a is greater than or less than alpha). This identification is accomplished by delineating the growth rate properties of the differenc...
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作者：De Monvel, AB; Khorunzhy, A
作者单位：Sorbonne Universite; Universite Paris Cite; National Academy of Sciences Ukraine; B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine; National Academy of Sciences Ukraine; B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine
摘要：We study the eigenvalue distribution of NxN symmetric random matrices H-N(x, y) = N(-1/2)h(x, y), x, y = 1,..., N, where h(x, y), x less than or equal to y are Gaussian weakly dependent random variables. We prove that the normalized eigenvalue counting function of H-N converges with probability 1 to a nonrandom function mu(lambda) as N --> infinity. We derive an equation for the Stieltjes transform of the measure d mu(lambda) and show that the latter has a compact support Lambda(mu). We find t...
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作者：Arnold, L; Imkeller, P
作者单位：University of Bremen; Humboldt University of Berlin
摘要：Let dx = Sigma(i=0)(m) A(i)x circle dW(i) be a linear SDE in R-d, generating the flow Phi(t), of Linear isomorphisms. The multiplicative ergodic theorem asserts that every vector v is an element of R-d \ {0} possesses a Lyapunov exponent (exponential gran th rate) lambda(v) under Phi(t), which is a random variable taking its values from a finite list of canonical exponents lambda(i) realized in the invariant Oseledets spaces E-i. We prove that, in the case of simple Lyapunov spectrum, every 2-...
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作者：Handjani, SJ
作者单位：University of Mississippi
摘要：We consider the d-dimensional threshold voter model. It is known that, except in the one-dimensional nearest-neighbor case, coexistence occurs (nontrivial invariant measures exist). In fact, there is a nontrivial limit eta(infinity)(1/2) Obtained by starting from the product measure with density 1/2. We show that in these coexistent cases, eta(t) double right arrow alpha delta(0) + beta delta(1) (1- alpha - beta)eta(infinity)(1/2) as t --> infinity, where alpha = P(tau(0) < infinity), beta = P...
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作者：De Santis, E; Gandolfi, A
作者单位：Sapienza University Rome; University of Rome Tor Vergata
摘要：We study occurrence and properties of percolation of occupied bonds in systems with random interactions and, hence, frustration. We develop a general argument, somewhat like Peierls' argument, by which we show that in Z(d), d greater than or equal to 2, percolation occurs for all possible interactions (provided they are bounded away from zero) if the parameter p is an element of (0, 1), regulating the density of occupied bonds, is high enough. If the interactions are i.i.d. random variables th...
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作者：Wang, QY; Jing, BY
作者单位：University of Wollongong; Hong Kong University of Science & Technology
摘要：In this paper we shall derive Exponential nonuniform Berry-Esseen bounds in the central limit theorem for self-normalized sums. We show that the size of the error can be reduced considerably by replacing the usual standardization by self-normalization. Tn particular, we establish the exponential bounds for the probability of the self-normalized sums under the condition that the third moment is finite, whereas an exponential moment assumption is required for the standardized sums. Applications ...
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作者：Osada, H; Spohn, H
作者单位：Nagoya University; Technical University of Munich; Technical University of Munich; University of Munich
摘要：We consider Brownian motion perturbed by the exponential of an action. The action is the sum of an external, one-body potential and a two-body interaction potential which depends only on the increments. Under suitable conditions on these potentials, we establish existence and uniqueness of the corresponding Gibbs measure. We also provide an example where uniqueness fails because of a slow decay in the interaction potential.
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作者：Boucher, C; Ellis, RS; Turkington, B
作者单位：Illinois Wesleyan University; University of Massachusetts System; University of Massachusetts Amherst
摘要：The main theorem is the large deviation principle for the doubly indexed sequence of random measures [GRAPHICS] Here theta is a probability measure on a Polish space K, {D-r, k, k = 1,...,2(r)} is a dyadic partition of K (hence the use of 2(r) summands) satisfying theta{D-r,D-k} = 1/2(r) and L-q,(1), L-q,(2),...,L-q, (2r) is an independent, identically distributed sequence of random probability measures on a Polish space Y such that {L-q,L-k, q is an element of N} satisfies the large deviation...
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作者：Mohammed, SEA; Scheutzow, MKR
作者单位：Southern Illinois University System; Southern Illinois University; Technical University of Berlin
摘要：We formulate and prove a local stable manifold theorem for stochastic differential equations (SDEs) that are driven by spatial Kunita-type semimartingales with stationary ergodic increments. Both Stratonovich and Ito-type equations are treated. Starting with the existence of a stochastic flow for a SDE, we introduce the notion of a hyperbolic stationary trajectory. We prove the existence of invariant random stable and unstable manifolds in the neighborhood of the hyperbolic stationary solution...
