Probability Theory and Related Fields

最新文章

• Explicit LDP for a slowed RW driven by a symmetric exclusion process AI翻译
  作者：Avena, L.; Jara, M.; Vollering, F.
  作者单位：Leiden University; Leiden University - Excl LUMC; Instituto Nacional de Matematica Pura e Aplicada (IMPA); University of Bath
  摘要：We consider a random walk (RW) driven by a simple symmetric exclusion process (SSE). Rescaling the RW and the SSE in such a way that a joint hydrodynamic limit theorem holds we prove a joint path large deviation principle. The corresponding large deviation rate function can be split into two components, the rate function of the SSE and the one of the RW given the path of the SSE. These components have different structures (Gaussian and Poissonian, respectively) and to overcome this difficulty ...
• Mass concentration and aging in the parabolic Anderson model with doubly-exponential tails AI翻译
  作者：Biskup, Marek; Koenig, Wolfgang; dos Santos, Renato S.
  作者单位：University of California System; University of California Los Angeles; Charles University Prague; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Technical University of Berlin
  摘要：We study the non-negative solution to the Cauchy problem for the parabolic equation on with initial data . Here is the discrete Laplacian on and is an i.i.d. random field with doubly-exponential upper tails. We prove that, for large t and with large probability, most of the total mass of the solution resides in a bounded neighborhood of a site that achieves an optimal compromise between the local Dirichlet eigenvalue of the Anderson Hamiltonian and the distance to the origin. The processes and...
• Hole probability for zeroes of Gaussian Taylor series with finite radii of convergence AI翻译
  作者：Buckley, Jeremiah; Nishry, Alon; Peled, Ron; Sodin, Mikhail
  作者单位：Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Instituto de Ciencia de Materiales de Madrid (ICMM); CSIC - Instituto de Ciencias Matematicas (ICMAT); University of Michigan System; University of Michigan; Tel Aviv University
  摘要：We study a family of random Taylor series F(z) = n= 0.nan zn with radius of convergence almost surely 1 and independent, identically distributed complex Gaussian coefficients ; these Taylor series are distinguished by the invariance of their zero sets with respect to isometries of the unit disk. We find reasonably tight upper and lower bounds on the probability that F does not vanish in the disk as . Our bounds take different forms according to whether the non-random coefficients grow, decay o...
• Lipschitz embeddings of random fields AI翻译
  作者：Basu, Riddhipratim; Sidoravicius, Vladas; Sly, Allan
  作者单位：Tata Institute of Fundamental Research (TIFR); International Centre for Theoretical Sciences, Bengaluru; New York University; NYU Shanghai; Princeton University
  摘要：We consider the problem of embedding one i.i.d. collection of Bernoulli random variables indexed by it was shown in Basu and Sly(Probab Theory Relat Fields 159:721-775, 2014) to be possible almost surely for sufficiently large M. In this paper we provide a multi-scale argument extending this result to higher dimensions.
• From Hammersley's lines to Hammersley's trees AI翻译
  作者：Basdevant, A. -L.; Gerin, L.; Gouere, J. -B.; Singh, A.
  作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Universite de Tours; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
  摘要：We construct a stationary random tree, embedded in the upper half plane, with prescribed offspring distribution and whose vertices are the atoms of a unit Poisson point process. This process which we call Hammersley's tree process extends the usual Hammersley's line process. Just as Hammersley's process is related to the problem of the longest increasing subsequence, this model also has a combinatorial interpretation: it counts the number of heaps (i.e. increasing trees) required to store a ra...
• Berry-Esseen bounds and Edgeworth expansions in the central limit theorem for transport distances AI翻译
  作者：Bobkov, Sergey G.
  作者单位：University of Minnesota System; University of Minnesota Twin Cities
  摘要：For sums of independent random variables , Berry-Esseen-type bounds are derived for the power transport distances in terms of Lyapunov coefficients . In the case of identically distributed summands, the rates of convergence are refined under Cram,r's condition.
• Learning without concentration for general loss functions AI翻译
  作者：Mendelson, Shahar
  作者单位：Technion Israel Institute of Technology; Australian National University
  摘要：We study the performance of empirical risk minimization in prediction and estimation problems that are carried out in a convex class and relative to a sufficiently smooth convex loss function. The framework is based on the small-ball method and thus is suited for heavy-tailed problems. Moreover, among its outcomes is that a well-chosen loss, calibrated to fit the noise level of the problem, negates some of the ill-effects of outliers and boosts the confidence level-leading to a gaussian like b...
• Importance sampling in path space for diffusion processes with slow-fast variables AI翻译
  作者：Hartmann, Carsten; Schuette, Christof; Weber, Marcus; Zhang, Wei
  作者单位：Free University of Berlin; Zuse Institute Berlin
  摘要：Importance sampling is a widely used technique to reduce the variance of a Monte Carlo estimator by an appropriate change of measure. In this work, we study importance sampling in the framework of diffusion process and consider the change of measure which is realized by adding a control force to the original dynamics. For certain exponential type expectation, the corresponding control force of the optimal change of measure leads to a zero-variance estimator and is related to the solution of a ...
• Higher order corrections for anisotropic bootstrap percolation AI翻译
  作者：Duminil-Copin, Hugo; van Enter, Aernout C. D.; Hulshof, Tim
  作者单位：Universite Paris Saclay; University of Geneva; University of Groningen; Eindhoven University of Technology
  摘要：We study the critical probability for the metastable phase transition of the two-dimensional anisotropic bootstrap percolation model with (1, 2)-neighbourhood and threshold r = 3. The first order asymptotics for the critical probability were recently determined by the first and second authors. Here we determine the following sharp second and third order asymptotics: We note that the second and third order terms are so large that the first order asymptotics fail to approximate pc even for latti...
• On the convergence of the extremal eigenvalues of empirical covariance matrices with dependence AI翻译
  作者：Chafai, Djalil; Tikhomirov, Konstantin
  作者单位：Universite PSL; Universite Paris-Dauphine; University of Alberta
  摘要：Consider a sample of a centered random vector with unit covariance matrix. We show that under certain regularity assumptions, and up to a natural scaling, the smallest and the largest eigenvalues of the empirical covariance matrix converge, when the dimension and the sample size both tend to infinity, to the left and right edges of the Marchenko-Pastur distribution. The assumptions are related to tails of norms of orthogonal projections. They cover isotropic log-concave random vectors as well ...