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作者：Berestycki, Nathanael; Laslier, Benoit; Ray, Gourab
作者单位：University of Vienna; Universite Paris Cite; University of Victoria
摘要：We show that the winding of the branches in a uniform spanning tree on a planar graph converge in the limit of fine mesh size to a Gaussian free field. The result holds assuming only convergence of simple random walk to Brownian motion and a Russo-Seymour-Welsh type crossing estimate, thereby establishing a strong form of universality. As an application, we prove universality of the fluctuations of the height function associated to the dimer model, in several situations. The proof relies on a ...
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作者：Nam, Kyeongsik
作者单位：University of California System; University of California Berkeley
摘要：We develop a unified theory to analyze the microcanonical ensembles with several constraints given by unbounded observables. Several interesting phenomena that do not occur in the single constraint case can happen under the multiple constraints case. We systematically analyze the detailed structures of such microcanonical ensembles in two orthogonal directions using the theory of large deviations. First of all, we establish the equivalence of ensembles result, which exhibits an interesting pha...
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作者：Angst, Jurgen; Poly, Guillaume
作者单位：Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We study the absolute continuity with respect to the Lebesgue measure of the distribution of the nodal volume associated with a smooth, nondegencrate and stationary Gaussian field (f (x), x is an element of R-d). Under mild conditions, we prove that in dimension d >= 3, the distribution of the nodal volume has an absolutely continuous component plus a possible singular part. This singular part is actually unavoidable bearing in mind that some Gaussian processes have a positive probability to k...
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作者：Jego, Antoine
作者单位：University of Vienna
摘要：We construct the analogue of Gaussian multiplicative chaos measures for the local times of planar Brownian motion by exponentiating the square root of the local times of small circles. We also consider a flat measure supported on points whose local time is within a constant of the desired thickness level and show a simple relation between the two objects. Our results extend those of (Ann. Probab. 22 (1994) 566-625), and in particular, cover the entire L-1-phase or subcritical regime. These res...
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作者：Valko, Benedek; Virag, Balint
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Toronto
摘要：We provide a precise coupling of the finite circular beta ensembles and their limit process via their operator representations. We prove explicit bounds on the distance of the operators and the corresponding point processes. We also prove an estimate on the beta-dependence of the Sine(beta) process.
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作者：Bobkov, S. G.; Chistyakov, G. P.; Goetze, F.
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Bielefeld
摘要：Under correlation-type conditions, we derive an upper bound of order (log n)/n for the average Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. The result is based on improved concentration inequalities on high-dimensional Euclidean spheres. Applications are illustrated on the example of log-concave probability measures.
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作者：Mareche, Laure; Martinelli, Fabio; Toninelli, Cristina
作者单位：Universite Paris Cite; Roma Tre University; Universite PSL; Universite Paris-Dauphine
摘要：Kinetically constrained models (KCM) are a class of interacting particle systems which represent a natural stochastic (and nonmonotone) counterpart of the family of cellular automata known as U-bootstrap percolation. A key issue for KCM is to identify the divergence of the characteristic time scales when the equilibrium density of empty sites, q, goes to zero. In (Ann. Probab. 47 (2019) 324-361; Comm. Math. Phys. 369 (2019) 761-809), a general scheme was devised to determine a sharp upper boun...
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作者：Meszaros, Andras
作者单位：Central European University
摘要：We extend Lyons's tree entropy theorem to general determinantal measures. As a byproduct we show that the sofic entropy of an invariant determinantal measure does not depend on the chosen sofic approximation.
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作者：Devraj, Adithya; Kontoyiannis, Ioannis; Meyn, Sean
作者单位：State University System of Florida; University of Florida; University of Cambridge
摘要：For a discrete-time Markov chain X = {X (t)} evolving on R-l with transition kernel P, natural, general conditions are developed under which the following are established: (i) The transition kernel P has a purely discrete spectrum, when viewed as a linear operator on a weighted Sobolev space L-infinity(v,1) of functions with norm, parallel to f parallel to(v,1) = sup(x is an element of Rl)1/v(x)max{vertical bar f (x)vertical bar,vertical bar partial derivative(1) f (x)vertical bar, ..., a vert...
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作者：Aidekon, Elie; Hu, Yueyun; Shi, Zhan
作者单位：Sorbonne Universite; Universite Paris Cite
摘要：It is well known (see Dvoretzky, Erdos and Kakutani (Bull. Res. Council Israel Sect. F 7F (1958) 175-180) and Le Gall (J. Funct. Anal. 71 (1987) 246-262)) that a planar Brownian motion (B-t)(t >= 0) has points of infinite multiplicity, and these points form a dense set on the range. Our main result is the construction of a family of random measures, denoted by {M-infinity(alpha)}(0<2), that are supported by the set of the points of infinite multiplicity. We prove that for any alpha is an eleme...
