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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...
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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...
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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：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...
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作者：Kulik, Alexei; Scheutzow, Michael
作者单位：National Academy of Sciences Ukraine; Institute of Mathematics of NASU; Technical University of Berlin
摘要：We provide sufficient conditions for the uniqueness of an invariant measure of a Markov process as well as for the weak convergence of transition probabilities to the invariant measure. Our conditions are formulated in terms of generalized couplings. We apply our results to several SPDEs for which unique ergodicity has been proven in a recent paper by Glatt-Holtz, Mattingly, and Richards and show that under essentially the same assumptions the weak convergence of transition probabilities actua...
