2期

最新文章

• SCALING LIMIT OF THE HOMOGENIZATION COMMUTATOR FOR GAUSSIAN COEFFICIENT FIELDS AI翻译
  作者：Duerinckx, Mitia; Fischer, Julian; Gloria, Antoine
  作者单位：Universite Libre de Bruxelles; Institute of Science & Technology - Austria; Sorbonne Universite; Universite Paris Cite
  摘要：Consider a linear elliptic partial differential equation in divergence form with a random coefficient field. The solution-operator displays fluctuations around its expectation. The recently-developed pathwise theory of fluctuations in stochastic homogenization reduces the characterization of these fluctuations to those of the so-called standard homogenization commutator. In this contribution, we investigate the scaling limit of this key quantity: starting from a Gaussian-like coefficient field...
• RARE EVENT ASYMPTOTICS FOR EXPLORATION PROCESSES FOR RANDOM GRAPHS AI翻译
  作者：Bhamidi, Shankar; Budhiraja, Amarjit; Dupuis, Paul; Wu, Ruoyu
  作者单位：University of North Carolina; University of North Carolina Chapel Hill; Brown University; Iowa State University
  摘要：Large deviations for random graph models has been a topic of significant recent research activity. Much work in this area is focused on the class of dense random graph models (number of edges in the graph scale as n(2), where n is the number of vertices) where the theory of graphons has emerged as a principal tool in the study of large deviation properties. These tools do not give a good approach to large deviation problems for random graph models in the sparse regime. The aim of this paper is...
• A SINGULAR TOEPLITZ DETERMINANT AND THE DISCRETE TACNODE KERNEL FOR SKEW-AZTEC RECTANGLES AI翻译
  作者：Adler, Mark; Johansson, Kurt; van Moerbeke, Pierre
  作者单位：Brandeis University; Royal Institute of Technology; Universite Catholique Louvain; Brandeis University
  摘要：Random tilings of geometrical shapes with dominos or lozenges have been a rich source of universal statistical distributions. This paper deals with domino tilings of checker board rectangular shapes such that the top two and bottom two adjacent squares have the same orientation and the two most left and two most right ones as well. It forces these so-called skew-Aztec rectangles to have cuts on either side. For large sizes of the domain and upon an appropriate scaling of the location of the cu...
• ON EXPLICIT L2-CONVERGENCE RATE ESTIMATE FOR PIECEWISE DETERMINISTIC MARKOV PROCESSES IN MCMC ALGORITHMS AI翻译
  作者：Lu, Jianfeng; Wang, Lihan
  作者单位：Duke University; Duke University; Duke University
  摘要：We establish L-2-exponential convergence rate for three popular piece-wise deterministic Markov processes for sampling: the randomized Hamiltonian Monte Carlo method, the zigzag process and the bouncy particle sampler. Our analysis is based on a variational framework for hypocoercivity, which combines a Poincare-type inequality in time-augmented state space and a standard L-2 energy estimate. Our analysis provides explicit convergence rate estimates, which are more quantitative than existing r...
• THE DIRECTIONAL OPTIMAL TRANSPORT AI翻译
  作者：Nutz, Marcel; Wang, Ruodu
  作者单位：Columbia University; University of Waterloo
  摘要：We introduce a constrained optimal transport problem where origins x can only be transported to destinations y >= x. Our statistical motivation is to describe the sharp upper bound for the variance of the treatment effect Y - X given marginals when the effect is monotone, or Y >= X. We thus focus on supermodular costs (or submodular rewards) and introduce a coupling P-* that is optimal for all such costs and yields the sharp bound. This coupling admits manifold characterizations-geometric, ord...
• RANDOM CONCAVE FUNCTIONS AI翻译
  作者：Baxendale, Peter; Wong, Ting-Kam Leonard
  作者单位：University of Southern California; University of Toronto
  摘要：Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave functions on the unit simplex measure the concentration of capital, and their gradient maps define novel investment strategies. The gradient maps may also be regarded as optimal transport maps on the simplex. In this paper we construct and study probability ...
• CORRELATED RANDOMLY GROWING GRAPHS AI翻译
  作者：Racz, Miklos Z.; Sridhar, Anirudh
  作者单位：Princeton University
  摘要：We introduce a new model of correlated randomly growing graphs and study the fundamental questions of detecting correlation and estimating aspects of the correlated structure. The model is simple and starts with any model of randomly growing graphs, such as uniform attachment (UA) or preferential attachment (PA). Given such a model, a pair of graphs (G(1), G(2)) is grown in two stages: until time t(*) they are grown together (i.e., G(1) = G(2)), after which they grow independently according to...
• A PROBABILISTIC APPROACH TO CONVEX (φ)-ENTROPY DECAY FOR MARKOV CHAINS AI翻译
  作者：Conforti, Giovanni
  作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
  摘要：We study the exponential dissipation of entropic functionals along the semigroup generated by a continuous time Markov chain and the associated convex Sobolev inequalities, including MLSI and Beckner inequalities. We propose a method that combines the Bakry-Emery approach and coupling arguments, which we use as a probabilistic alternative to the discrete Bochner identities. In particular, the validity of the method is not limited to the perturbative setting and we establish convex entropy deca...
• A CLASSIFICATION OF THE DYNAMICS OF THREE-DIMENSIONAL STOCHASTIC ECOLOGICAL SYSTEMS AI翻译
  作者：Hening, Alexandru; Nguyen, Dang H.; Schreiber, Sebastian J.
  作者单位：Tufts University; University of Alabama System; University of Alabama Birmingham; University of California System; University of California Davis
  摘要：The classification of the long-term behavior of dynamical systems is a fundamental problem in mathematics. For both deterministic and stochastic dynamics specific classes of models verify Palis' conjecture: the long-term behavior is determined by a finite number of stationary distributions. In this paper we consider the classification problem for stochastic models of interacting species. For a large class of three-species, stochastic differential equation models, we prove a variant of Palis' c...
• ARE AMERICAN OPTIONS EUROPEAN AFTER ALL? AI翻译
  作者：Christensen, Soeren; Kallsen, Jan; Lenga, Matthias
  作者单位：University of Kiel; Bayer AG
  摘要：We call a given American option representable if there exists a European claim which dominates the American payoff at any time and such that the values of the two options coincide in the continuation region of the American option. This concept has interesting implications from a probabilistic, analytic, financial, and numeric point of view. Relying on methods from (Math. Finance 24 (2014) 156-172; Ann. Inst. H. Poincare Anal. Non Lineaire 18 (2001) 1-17; Ann. Appl. Probab. 12 (2002) 196-223) a...