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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：Cipriani, Alessandra; Hazra, Rajat Subhra; Ruszel, Wioletta M.
作者单位：University of Bath; Indian Statistical Institute; Indian Statistical Institute Kolkata; Delft University of Technology
摘要：In a recent work Levine et al. (Ann Henri Poincare 17:1677-1711, 2016. 10.1007/s00023-015-0433-x) prove that the odometer function of a divisible sandpile model on a finite graph can be expressed as a shifted discrete bilaplacian Gaussian field. For the discrete torus, they suggest the possibility that the scaling limit of the odometer may be related to the continuum bilaplacian field. In this work we show that in any dimension the rescaled odometer converges to the continuum bilaplacian field...
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作者：Lei, Lihua; Bickel, Peter J.; El Karoui, Noureddine
作者单位：University of California System; University of California Berkeley
摘要：We investigate the asymptotic distributions of coordinates of regression M-estimates in the moderate p/n regime, where the number of covariates p grows proportionally with the sample size n. Under appropriate regularity conditions, we establish the coordinate-wise asymptotic normality of regression M-estimates assuming a fixed-design matrix. Our proof is based on the second-order Poincare inequality and leave-one-out analysis. Some relevant examples are indicated to show that our regularity co...
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作者：Angel, Omer; Ray, Gourab
作者单位：University of British Columbia; University of Cambridge
摘要：We prove that the half plane version of the uniform infinite planar triangulation (UIPT) is recurrent. The key ingredients of the proof are a construction of a new full plane extension of the half plane UIPT, based on a natural decomposition of the half plane UIPT into independent layers, and an extension of previous methods for proving recurrence of weak local limits (while still using circle packings).
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作者：van Handel, Ramon
作者单位：Princeton University
摘要：A precise description of the convexity of Gaussian measures is provided by sharp Brunn-Minkowski type inequalities due to Ehrhard and Borell. We show that these are manifestations of a game-theoretic mechanism: a minimax variational principle for Brownian motion. As an application, we obtain a Gaussian improvement of Barthe's reverse Brascamp-Lieb inequality.
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作者：Duminil-Copin, H.; Tassion, V.; Teixeira, A.
作者单位：Universite Paris Saclay; University of Geneva
摘要：We consider critical oriented Bernoulli percolation on the square lattice . We prove a Russo-Seymour-Welsh type result which allows us to derive several new results concerning the critical behaviorWe establish that the probability that the origin is connected to distance n decays polynomially fast in n. We prove that the critical cluster of 0 conditioned to survive to distance n has a typical width satisfying for some . The sub- linear polynomial fluctuations contrast with the supercritical re...
