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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...
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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...
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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：Goncalves, Patricia; Jara, Milton
作者单位：Universidade de Lisboa
摘要：We show that the stationary density fluctuations of exclusion processes with long jumps, whose rates are of the form where depends on the sign of , are given by a fractional Ornstein-Uhlenbeck process for . When we show that the density fluctuations are tight, in a suitable topology, and that any limit point is an energy solution of the fractional Burgers equation, previously introduced in Gubinelli and Jara (Stoch Partial Differ Equ Anal Comput 1(2):325-350, 2013) in the finite volume setting.
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作者：Buckley, Jeremiah; Feldheim, Naomi
作者单位：University of London; King's College London; Weizmann Institute of Science
摘要：This paper studies the winding of a continuously differentiable Gaussian stationary process f : R. C in the interval [0, T]. We give formulae for the mean and the variance of this random variable. The variance is shown to always grow at least linearly with T, and conditions for it to be asymptotically linear or quadratic are given. Moreover, we show that if the covariance function together with its second derivative are in L2( R), then the winding obeys a central limit theorem. These results c...
