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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.
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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...
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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.
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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...
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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 ...
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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...
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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 ...
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作者：Bertoin, Jean; Budd, Timothy; Curien, Nicolas; Kortchemski, Igor
作者单位：University of Zurich; University of Copenhagen; Niels Bohr Institute; CEA; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique
摘要：The purpose of the present work is twofold. First, we develop the theory of general self-similar growth-fragmentation processes by focusing on martingales which appear naturally in this setting and by recasting classical results for branching random walks in this framework. In particular, we establish many-to-one formulas for growth-fragmentations and define the notion of intrinsic area of a growth-fragmentation. Second, we identify a distinguished family of growth-fragmentations closely relat...
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作者：Beiglboeck, Mathias; Eder, Manu; Elgert, Christiane; Schmock, Uwe
作者单位：University of Vienna; Technische Universitat Wien
摘要：We adapt ideas and concepts developed in optimal transport (and its martingale variant) to give a geometric description of optimal stopping times t of Brownian motion subject to the constraint that the distribution of t is a given probability mu. The methods work for a large class of cost processes. (At a minimum we need the cost process to be measurable and (F0 t) t= 0-adapted. Continuity assumptions can be used to guarantee existence of solutions.) We find that for many of the cost processes...
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作者：Borodin, Alexei; Corwin, Ivan; Ferrari, Patrik L.
作者单位：Massachusetts Institute of Technology (MIT); Columbia University; University of Bonn
摘要：We consider a discrete model for anisotropic (2 + 1)-dimensional growth of an interface height function. Owing to a connection with q-Whittaker functions, this system enjoys many explicit integral formulas. By considering certain Gaussian stochastic differential equation limits of the model we are able to prove a space-time limit of covariances to those of the (2+ 1)-dimensional additive stochastic heat equation (or Edwards-Wilkinson equation) along characteristic directions. In particular, th...
