Probability Theory and Related Fields

最新文章

• Essential spectral radius for Markov semigroups (I): discrete time case AI翻译
  作者：Wu, LM
  作者单位：Wuhan University
  摘要：Using two new measures of non-compactness beta(tau) (P) and beta(w) (P) for a positive kernel P on a Polish space E, we obtain a new formula of Nussbaum-Gelfand type for the essential spectral radius r(ess) (P) on bB. Using that formula we show that different known sufficient conditions for geometric ergodicity such as Doeblin's condition, drift condition by means of Lyapunov function, geometric recurrence etc lead to variational formulas of the essential spectral radius. All those can be easi...
• Area versus capacity and solidification in the crushed ice model AI翻译
  作者：van den Berg, M; Bolthausen, E
  作者单位：University of Bristol; University of Zurich
• Distribution of the shape of Markovian random words AI翻译
  作者：Chistyakov, GP; Götze, F
  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; University of Bielefeld
  摘要：The distribution of the shape lambda of the semi-standard tableau of a random word in k letters is asymptotically given by the distribution of the spectrum of a random traceless kxk Gaussian Unitary Ensemble (GUE) matrix provided that these letters are independent with uniform distribution. Kuperberg (2002) conjectured that this result by Johansson (2001) remains valid if the letters of the word are generated by an irreducible Markov chain on the alphabet with cyclic transition matrix. In this...
• Central limit theorems for the large-spin asymptotics of quantum spins AI翻译
  作者：Michoel, T; Nachtergaele, B
  作者单位：KU Leuven; University of California System; University of California Davis
  摘要：We use a generalized form of Dyson's spin wave formalism to prove several central limit theorems for the large-spin asymptotics of quantum spins in a coherent state.
• Correlations for superpositions and decimations of Laguerre and Jacobi orthogonal matrix ensembles with a parameter AI翻译
  作者：Forrester, PJ; Rains, EM
  作者单位：University of Melbourne; AT&T
  摘要：A superposition of a matrix ensemble refers to the ensemble constructed from two independent copies of the original, while a decimation refers to the formation of a new ensemble by observing only every second eigenvalue. In the cases of the classical matrix ensembles with orthogonal symmetry, it is known that forming superpositions and decimations gives rise to classical matrix ensembles with unitary and symplectic symmetry. The basic identities expressing these facts can be extended to includ...
• The principle of penalized empirical risk in severely ill-posed problems AI翻译
  作者：Golubev, Y
  作者单位：Aix-Marseille Universite
  摘要：We study a standard method of regularization by projections of the linear inverse problem Y=Ax+epsilon, where epsilon is a white Gaussian noise, and A is a known compact operator. It is assumed that the eigenvalues of AA(*) converge to zero with exponential decay. Such behavior of the spectrum is typical for inverse problems related to elliptic differential operators. As model example we consider recovering of unknown boundary conditions in the Dirichlet problem for the Laplace equation on the...
• Quenched invariance principles for walks on clusters of percolation or among random conductances AI翻译
  作者：Sidoravicius, V; Sznitman, AS
  作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA); Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：In this work we principally study random walk on the supercritical infinite cluster for bond percolation on Z(d). We prove a quenched functional central limit theorem for the walk when dgreater than or equal to4. We also prove a similar result for random walk among i.i.d. random conductances along nearest neighbor edges of Z(d), when dgreater than or equal to1.
• Fisher information inequalities and the central limit theorem AI翻译
  作者：Johnson, O; Barron, A
  作者单位：University of Cambridge; Yale University
  摘要：We give conditions for an O(1/n) rate of convergence of Fisher information and relative entropy in the Central Limit Theorem. We use the theory of projections in L-2 spaces and Poincare inequalities, to provide a better understanding of the decrease in Fisher information implied by results of Barron and Brown. We show that if the standardized Fisher information ever becomes finite then it converges to zero.
• Time-fractional telegraph equations and telegraph processes with Brownian time AI翻译
  作者：Orsingher, E; Beghin, L
  作者单位：Sapienza University Rome
  摘要：We study the fundamental solutions to time-fractional telegraph equations of order 2alpha. We are able to obtain the Fourier transform of the solutions for any alpha and to give a representation of their inverse, in terms of stable densities. For the special case alpha=1/2, we can show that the fundamental solution is the distribution of a telegraph process with Brownian time. In a special case, this becomes the density of the iterated Brownian motion, which is therefore the fundamental soluti...
• The Brownian loop soup AI翻译
  作者：Lawler, GF; Werner, W
  作者单位：Cornell University; Universite Paris Saclay
  摘要：We define a natural conformally invariant measure on unrooted Brownian loops in the plane and study some of its properties. We relate this measure to a measure on loops rooted at a boundary point of a domain and show how this relation gives a way to chronologically add Brownian loops to simple curves in the plane.