3-4期

最新文章

• Boundary proximity of SLE AI翻译
  作者：Schramm, Oded; Zhou, Wang
  作者单位：National University of Singapore; Microsoft
  摘要：This paper examines how close the chordal SLEk curve gets to the real line asymptotically far away from its starting point. In particular, when k is an element of (0, 4), it is shown that if beta > beta(k) := 1/(8/k - 2), then the intersection of the SLEk curve with the graph of the function y = x/(log x)(beta), x > e, is a.s. bounded, while it is a.s. unbounded if beta = beta(k). The critical SLE4 curve a.s. intersects the graph of y = x(-(log log x)alpha), x > e(e), in an unbounded set if al...
• Wasserstein space over the Wiener space AI翻译
  作者：Fang, Shizan; Shao, Jinghai; Sturm, Karl-Theodor
  作者单位：University of Bonn; Universite Bourgogne Europe; Beijing Normal University
  摘要：The goal of this paper is to study optimal transportation problems and gradient flows of probability measures on the Wiener space, based on and extending fundamental results of Feyel-stunel. Carrying out the program of Ambrosio-Gigli-Savar,, we present a complete characterization of the derivative processes for certain class of absolutely continuous curves. We prove existence of the gradient flow curves for the relative entropy w.r.t. the Wiener measure and identify these gradient flow curves ...
• Spin glasses and Stein's method AI翻译
  作者：Chatterjee, Sourav
  作者单位：University of California System; University of California Berkeley
  摘要：We introduce some applications of Stein's method in the high temperature analysis of spin glasses. Stein's method allows the direct analysis of the Gibbs measure without having to eate a cavity. Another advantage is that it gives limit theorems with total variation error bounds, although the bounds can be suboptimal. A surprising byproduct of our analysis is a relatively transparent explanation of the Thouless-Anderson-Palmer system of equations. Along the way, we develop Stein's method for mi...
• Survival of contact processes on the hierarchical group AI翻译
  作者：Athreya, Siva R.; Swart, Jan M.
  作者单位：Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences; Indian Statistical Institute; Indian Statistical Institute Bangalore
  摘要：We consider contact processes on the hierarchical group, where sites infect other sites at a rate depending on their hierarchical distance, and sites become healthy with a constant recovery rate. If the infection rates decay too fast as a function of the hierarchical distance, then we show that the critical recovery rate is zero. On the other hand, we derive sufficient conditions on the speed of decay of the infection rates for the process to exhibit a nontrivial phase transition between extin...
• Large deviation for stochastic line integrals as L p -currents AI翻译
  作者：Kusuoka, Shigeo; Kuwada, Kazumasa; Tamura, Yozo
  作者单位：Ochanomizu University; University of Tokyo; Keio University
  摘要：The large deviation principle for stochastic line integrals along Brownian paths on a compact Riemannian manifold is studied. We regard them as a random map on a Sobolev space of 1-forms. We show that the differentiability order of the Sobolev space can be chosen to be almost independent of the dimension of the underlying space by assigning higher integrability on 1-forms. The large deviation is formulated for the joint distribution of stochastic line integrals and the empirical distribution o...
• A generalized Neyman-Pearson lemma for g-probabilities AI翻译
  作者：Ji, Shaolin; Zhou, Xun Yu
  作者单位：Shandong University; University of Oxford; Chinese University of Hong Kong
  摘要：This paper is concerned with hypothesis tests for g-probabilities, a class of nonlinear probability measures. The problem is shown to be a special case of a general stochastic optimization problem where the objective is to choose the terminal state of certain backward stochastic differential equations so as to minimize a g-expectation. The latter is solved with a stochastic maximum principle approach. Neyman-Pearson type results are thereby derived for the original problem with both simple and...
• The root-unroot algorithm for density estimation as implemented via wavelet block thresholding AI翻译
  作者：Brown, Lawrence; Cai, Tony; Zhang, Ren; Zhao, Linda; Zhou, Harrison
  作者单位：University of Pennsylvania; Yale University
  摘要：We propose and implement a density estimation procedure which begins by turning density estimation into a nonparametric regression problem. This regression problem is created by binning the original observations into many small size bins, and by then applying a suitable form of root transformation to the binned data counts. In principle many common nonparametric regression estimators could then be applied to the transformed data. We propose use of a wavelet block thresholding estimator in this...