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作者：Eisenbaum, Nathalie
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
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作者：Banerjee, Sayan; Budhiraja, Amarjit
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：The infinite Atlas model describes a countable system of competing Brownian particles where the lowest particle gets a unit upward drift and the rest evolve as standard Brownian motions. The stochastic process of gaps between the particles in the infinite Atlas model does not have a unique stationary distribution and in fact for every a >= 0, pi(a) := circle times(infinity)(i=1) Exp(2 + ia) is a stationary measure for the gap process. We say that an initial distribution of gaps is in the weak ...
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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：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：Legrand, Alexandre; Petrelis, Nicolas
作者单位：Nantes Universite
摘要：The present paper is dedicated to the 2-dimensional Interacting Partially Directed Self Avoiding Walk constrained to remain in the upper-half plane and interacting with the horizontal axis. This model has originally been introduced to investigate the behavior of a homopolymer dipped in a poor solvent and adsorbed along a horizontal hard wall. It is known to undergo a collapse transition between an extended phase, inside which typical configurations of the polymer have a large horizontal extens...
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作者：Pitman, Jim; Tang, Wenpin
作者单位：University of California System; University of California Berkeley; Columbia University
摘要：This paper is concerned with the limit laws of the extreme order statistics derived from a symmetric Laplace walk. We provide two different descriptions of the point process of the limiting extreme order statistics: a branching representation and a squared Bessel representation. These complementary descriptions expose various hidden symmetries in branching processes and Brownian motion which lie behind some striking formulas found by Schehr and Majumdar (Phys. Rev. Lett. 108 (2012) 040601). In...
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作者：Goldman, Michael; Huesmann, Martin
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); University of Munster
摘要：The aim of this paper is to justify in dimensions two and three the ansatz of Caracciolo et al. stating that the displacement in the optimal matching problem is essentially given by the solution to the linearized equation that is, the Poisson equation. Moreover, we prove that at all mesoscopic scales, this displacement is close in suitable negative Sobolev spaces to a curl-free Gaussian free field. For this, we combine a quantitative estimate on the difference between the displacement and the ...
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作者：Liu, Zhipeng
作者单位：University of Kansas
摘要：Recently Johansson and Rahman obtained the limiting multitime distribution for the discrete polynuclear growth model (Johansson and Rahman (2019)), which is equivalent to a discrete TASEP model with step initial condition. In this paper, we obtain a finite time multipoint distribution formula of continuous TASEP with general initial conditions in the space-time plane. We evaluate the limit of this distribution function when the times go to infinity at the same speed for both step and flat init...
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作者：Borga, Jacopo; Maazoun, Mickael
作者单位：University of Zurich; Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：Baxter permutations, plane bipolar orientations, and a specific family of walks in the nonnegative quadrant, called tandem walks, are well-known to be related to each other through several bijections. We introduce a further new family of discrete objects, called coalescent-walk processes and we relate it to the three families mentioned above. We prove joint Benjamini-Schramm convergence (both in the annealed and quenched sense) for uniform objects in the four families. Furthermore, we explicit...
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作者：Sly, Allan; Zhang, Lingfu
作者单位：Princeton University
摘要：For the Voter Model on Z(d), d >= 3, we show that the (extremal) stationary distributions are isomorphic to Bernoulli shifts, and answer an open question asked by Steif and Tykesson in (ALEA Lat. Am. J. Probab. Math. Stat. 16 (2019) 899-955). The proof gives explicit constructions of the stationary distributions as factors of IID processes on Z(d).
