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作者：Elentano, Michael
作者单位：University of California System; University of California Berkeley
摘要：We develop an approach for studying the local convexity of a certain class of random objectives around the iterates of an AMP algorithm. Our approach involves applying the Sudakov-Fernique inequality conditionally on a long sequence of AMP iterates, and our main contribution is to demonstrate the way in which the resulting objective can be simplified and analyzed. As a consequence, we provide a new, and arguably simpler, proof of some of the results of Celentano, Fan and Mei ( Ann. Statist. 51...
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作者：Fehrman, Benjamin
作者单位：University of Oxford
摘要：We prove that diffusion equations with a space-time stationary and ergodic, divergence -free drift homogenize in law to a deterministic stochastic partial differential equation with Stratonovich transport noise. In the absence of spatial ergodicity, the drift is only partially absorbed into the skewsymmetric part of the flux through the use of an appropriately defined stream matrix. This leaves a time -dependent, spatially -homogenous transport which, for mildly decorrelating fields, converges...
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作者：Herry, Ronan; Malicet, Dominique; Poly, Guillaume
作者单位：Universite de Rennes; Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：We establish, in full generality, an unexpected phenomenon of strong regularization along normal convergence on Wiener chaoses. Namely, for every sequence of chaotic random variables, convergence in law to the Gaussian distribution is automatically upgraded to superconvergence : the regularity of the densities increases along the convergence, and all the derivatives converge uniformly on the real line. Our findings strikingly strengthen known results regarding modes of convergence for normal a...
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作者：Van Engelenburg, Diederik; Hutchcroft, Tom
作者单位：University of Vienna; California Institute of Technology
摘要：We prove that if a unimodular random rooted graph is recurrent, the number of ends of its uniform spanning tree is almost surely equal to the number of ends of the graph. Together with previous results in the transient case, this completely resolves the problem of the number of ends of wired uniform spanning forest components in unimodular random rooted graphs and confirms a conjecture of Aldous and Lyons (2006).
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作者：Beliaev, Dmitry; Mcauley, Michael; Muirhead, Stephen
作者单位：University of Oxford; University of Helsinki; University of Melbourne
摘要：3 School of Mathematics and Statistics, University of Melbourne, c smui@unimelb.edu.au For a smooth stationary Gaussian field f on R d and level is an element of R, we consider the number of connected components of the excursion set { f >= } (or level set { f = } ) contained in large domains. The mean of this quantity is known to scale like the volume of the domain under general assumptions on the field. We prove that, assuming sufficient decay of correlations (e.g., the Bargmann-Fock field), ...
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作者：Gwynne, Ewain; Pfeffer, Joshua; Park, Minjae
作者单位：University of Chicago; Columbia University
摘要：We study the Loewner evolution whose driving function is W-t = B-t(1) + iB(t)(2), where (B-1, B-2) is a pair of Brownian motions with a given covariance matrix. This model can be thought of as a generalization of Schramm-Loewner evolution (SLE) with complex parameter values. We show that our Loewner evolutions behave very differently from ordinary SLE. For example, if neither B-1 nor B-2 is identically equal to zero, then the set of points disconnected from infinity by the Loewner hull has non...
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作者：Friz, Peter K.; Zorin-Kranich, Pavel
作者单位：Technical University of Berlin; University of Bonn
摘要：We establish a new scale of p-variation estimates for martingale para-products, martingale transforms and Ito integrals, of relevance in rough paths theory, stochastic and harmonic analysis. As an application, we introduce rough semimartingales, a common generalization of classical semimartin-gales and (controlled) rough paths and their integration theory.
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作者：Caravenna, Francesco; Sun, Rongfeng; Zygouras, Nikos
作者单位：University of Milano-Bicocca; National University of Singapore; University of Warwick
摘要：The critical 2d stochastic heat flow (SHF) is a stochastic process of ran-dom measures on R2, recently constructed in (Invent. Math. 233 (2023) 325- 460). We show that this process falls outside the class of Gaussian multiplica-tive chaos (GMC), in the sense that it cannot be realised as the exponential of a (generalised) Gaussian field. We achieve this by deriving strict lower bounds on the moments of the SHF that are of independent interest.
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作者：Priola, Enrico
作者单位：University of Pavia
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作者：Taggia, Lorenzo
作者单位：Sapienza University Rome
摘要：We prove that in wide generality the critical curve of the activated random walk model is a continuous function of the deactivation rate, and we provide a bound on its slope, which is uniform with respect to the choice of the graph. Moreover, we derive strict monotonicity properties for the probability of a wide class of increasing events, extending previous results of (Invent. Math. 188 (2012) 127-150). Our proof method is of independent interest and can be viewed as a reformulation of the 'e...
