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作者：Caravenna, Francesco; den Hollander, Frank
作者单位：University of Milano-Bicocca; Leiden University - Excl LUMC; Leiden University
摘要：We consider a directed polymer of length N interacting with a linear interface. The monomers carry i.i.d. random charges (omega(i))(i=1)(N) taking values in R with mean zero and variance one. Each monomer i contributes an energy (beta omega(i) - h)phi(S-i) to the interaction Hamiltonian, where S-i is an element of Z is the height of monomer i with respect to the interface, phi : Z -> [0, infinity) is the interaction potential, beta is an element of [0, infinity) is the inverse temperature, and...
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作者：Cipolloni, Giorgio; Erdos, Laszlo; Schroeder, Dominik
作者单位：Institute of Science & Technology - Austria; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider large non-Hermitian real or complex random matrices X with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix elements of X are Gaussian. This result is the non-Hermitian counterpart of the universality of the Tracy-Widom distribution at the spectral edges of the Wigner ensemble.
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作者：Marciniak, Mikolaj; Maslanka, Lukasz; Sniady, Piotr
作者单位：Nicolaus Copernicus University; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
摘要：We consider the Robinson-Schensted-Knuth algorithm applied to a random input and investigate the shape of the bumping route (in the vicinity of the y-axis) when a specified number is inserted into a large Plancherel-distributed random tableau. We show that after a projective change of the coordinate system the bumping route converges in distribution to the Poisson process.
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作者：Dussaule, Matthieu; Gekhtman, Ilya
作者单位：Nantes Universite; Technion Israel Institute of Technology
摘要：Let Gamma be a relatively hyperbolic group and let mu be an admissible symmetric finitely supported probability measure on Gamma. We extend Floyd-Ancona type inequalities from Gekhtman et al. (Martin boundary covers Floyd boundary, 2017. arXiv:1708.02133) up to the spectral radius R of mu. We use them to find the precise homeomorphism type of the r-Martin boundary, which describes r-harmonic functions, for every r <= R. We also define a notion of spectral degeneracy along parabolic subgroups w...
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作者：Qian, Wei
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Universite Paris Saclay
摘要：We introduce and compute the generalized disconnection exponents eta(kappa)(beta) which depend on kappa is an element of (0, 4] and another real parameter beta, extending the Brownian disconnection exponents (corresponding to kappa = 8/3) computed by Lawler, Schramm and Werner (Acta Math 187(2):275-308, 2001; Acta Math 189(2):179-201, 2002) [conjectured by Duplantier and Kwon (Phys Rev Lett 61:2514-2517, 1988)]. For kappa is an element of (8/3, 4], the generalized disconnection exponents have ...
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作者：Chatterjee, Sourav; Diaconis, Persi
作者单位：Stanford University; Stanford University
摘要：We show that the convergence of finite state space Markov chains to stationarity can often be considerably speeded up by alternating every step of the chain with a deterministic move. Under fairly general conditions, we show that not only do such schemes exist, they are numerous.
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作者：Gubinelli, Massimiliano; Perkowski, Nicolas
作者单位：University of Bonn; University of Bonn; Free University of Berlin
摘要：We develop a martingale approach for a class of singular stochastic PDEs of Burgers type (including fractional and multi-component Burgers equations) by constructing a domain for their infinitesimal generators. It was known that the domainmust have trivial intersection with the usual cylinder test functions, and to overcome this difficulty we import some ideas from paracontrolled distributions to an infinite dimensional setting in order to construct a domain of controlled functions. Using the ...
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作者：Wong, Mo Dick
作者单位：University of Oxford
摘要：In this article we study the tail probability of the mass of Gaussian multiplicative chaos. With the novel use of a Tauberian argument and Goldie's implicit renewal theorem, we provide a unified approach to general log-correlated Gaussian fields in arbitrary dimension and derive precise first order asymptotics of the tail probability, resolving a conjecture of Rhodes and Vargas. The leading order is described by a universal constant that captures the generic property of Gaussian multiplicative...
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作者：Ahidar-Coutrix, A.; Le Gouic, T.; Paris, Q.
作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); HSE University (National Research University Higher School of Economics)
摘要：This paper provides rates of convergence for empirical (generalised) barycenters on compact geodesic metric spaces under general conditions using empirical processes techniques. Our main assumption is termed a variance inequality and provides a strong connection between usual assumptions in the field of empirical processes and central concepts of metric geometry. We study the validity of variance inequalities in spaces of non-positive and non-negative Aleksandrov curvature. In this last scenar...
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作者：Belius, David; Rosen, Jay; Zeitouni, Ofer
作者单位：University of Basel; City University of New York (CUNY) System; College of Staten Island (CUNY); Weizmann Institute of Science; New York University
