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作者：Ang, Morris; Park, Minjae; Pfeffer, Joshua; Sheffield, Scott
作者单位：Massachusetts Institute of Technology (MIT); Columbia University
摘要：We explore the geometric meaning of the so-called zeta-regularized determinant of the Laplace-Beltrami operator on a compact surface, with or without boundary. We relate the (-c/2)th power of the determinant of the Laplacian to the appropriately regularized partition function of a Brownian loop soup of intensity c on the surface. This means that, in a certain sense, decorating a random surface by a Brownian loop soup of intensity c corresponds to weighting the law of the surface by the (-c/2)t...
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作者：de Raphelis, Loic
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We consider a random walk on a Galton-Watson tree in random environment, in the subdiffusive case. We prove the convergence of the renormalised height function of the walk towards the continuous-time height process of a spectrally positive strictly stable Levy process, jointly with the convergence of the renormalised trace of the walk towards the real tree coded by the latter continuous-time height process.
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作者：Giunti, Arianna; Gu, Chenlin; Mourrat, Jean-Christophe
作者单位：Imperial College London; Universite PSL; Ecole Normale Superieure (ENS); New York University
摘要：For a class of interacting particle systems in continuous space, we show that finite-volume approximations of the bulk diffusion matrix converge at an algebraic rate. The models we consider are reversible with respect to the Poisson measures with constant density, and are of nongradient type. Our approach is inspired by recent progress in the quantitative homogenization of elliptic equations. Along the way, we develop suitable modifications of the Caccioppoli and multiscale Poincare inequaliti...
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作者：Kenyon, Richard; Pohoata, Cosmin
作者单位：Yale University
摘要：Given a graph g and collection of subgraphs T (called tiles), we consider covering g with copies of tiles in T so that each vertex v is an element of( )G is covered with a predetermined multiplicity. The multinomial tiling model is a natural probability measure on such configurations (it is the uniform measure on standard tilings of the corresponding blow-up of G). In the limit of large multiplicities, we compute the asymptotic growth rate of the number of multinomial tilings. We show that the...
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作者：Friz, Peter K.; Gatheral, Jim; Radoicic, Rados
作者单位：Technical University of Berlin; City University of New York (CUNY) System; Baruch College (CUNY)
摘要：This work is concerned with forest and cumulant type expansions of general random variables on a filtered probability space. We establish a broken exponential martingale expansion that generalizes and unifies the exponentiation result of Alos, Gatheral, and Radoicic (SSRN'17; Quant. Finance 20 (2020) 13-27) and the cumulant recursion formula of Lacoin, Rhodes, and Vargas (arXiv; (2019)). Specifically, we exhibit the two previous results as lower dimensional projections of the same generalized ...
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作者：Bednorz, Witold; Martynek, Rafal
作者单位：University of Warsaw
摘要：In this paper we complete the full characterization of the expected suprema of infinitely divisible processes. In particular, we remove the technical assumption called H(C-0, delta) condition and settle positively the conjecture posed by M. Talagrand.
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作者：Dauvergne, Duncan
作者单位：Princeton University
摘要：Last passage percolation and directed polymer models on Z(2) are invariant under translation and certain reflections. When these models have an integrable structure coming from either the RSK correspondence or the geometric RSK correspondence (e.g., geometric last passage percolation or the log-gamma polymer), we show that these basic invariances can be combined with a decoupling property to yield a rich new set of symmetries. Among other results, we prove shift and rearrangement invariance st...
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作者：Budzinski, Thomas; Lehericy, Thomas
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); University of Zurich
摘要：We study the simple random walk on the Uniform Infinite Half-Plane Map, which is the local limit of critical Boltzmann planar maps with a large and simple boundary. We prove that the simple random walk is recurrent, and that the resistance between the root and the boundary of the hull of radius r is at least of order log r . This resistance bound is expected to be sharp, and is better than those following from previous proofs of recurrence for nonbounded-degree planar maps models. Our main too...
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作者：Budzinski, Thomas; Louf, Baptiste
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); Uppsala University
摘要：We study the local limits of uniform high genus bipartite maps with prescribed face degrees. We prove the convergence toward a family of infinite maps of the plane, the q-IBPMs, which exhibit both a spatial Markov property and a hyperbolic behaviour. Therefore, we observe a similar local behaviour for a wide class of models of random high genus maps which can be seen as a result of universality. Our results cover all the regimes where the expected degree of the root face remains finite in the ...
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作者：Lacoin, Hubert
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：Gaussian multiplicative chaos (GMC) is informally defined as a random measure e(gamma X) dx where X is Gaussian field on R-d (or an open subset of it) whose correlation function is of the form K(x, y) = log 1/vertical bar y-x vertical bar + L(x, y), where L is a continuous function of x and y and gamma = alpha + i beta is a complex parameter. In the present paper we consider the case gamma is an element of P-III', where P-III':= {alpha + i beta : alpha, gamma is an element of R, vertical bar a...
