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作者：Oh, Tadahiro; Tzvetkov, Nikolay
作者单位：University of Edinburgh; Heriot Watt University; University of Edinburgh; CY Cergy Paris Universite
摘要：We consider the cubic fourth order nonlinear Schrodinger equation on the circle. In particular, we prove that the mean-zero Gaussian measures on Sobolev spaces , , are quasi-invariant under the flow.
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作者：Sinclair, Alistair; Srivastava, Piyush; Stefankovic, Daniel; Yin, Yitong
作者单位：University of California System; University of California Berkeley; California Institute of Technology; University of Rochester; Nanjing University
摘要：We study the problem of deterministic approximate counting of matchings and independent sets in graphs of bounded connective constant. More generally, we consider the problem of evaluating the partition functions of the monomer-dimer model (which is defined as a weighted sum over all matchings where each matching is given a weight in terms of a fixed parameter called the monomer activity) and the hard core model (which is defined as a weighted sum over all independent sets where an independent...
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作者：Georgiou, Nicos; Rassoul-Agha, Firas; Seppalainen, Timo
作者单位：University of Sussex; Utah System of Higher Education; University of Utah; University of Wisconsin System; University of Wisconsin Madison
摘要：We study the directed last-passage percolation model on the planar integer lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside the class of exactly solvable models. In Georgiou et al. (Probab Theory Relat Fields, 2016, doi:10.1007/s00440-016-0729-x) we constructed stationary cocycles and Busemann functions for this model. Using these objects, we prove new results on the competition interface, on existence, uniqueness, and coalescence of directional semi-infi...
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作者：Friz, Peter K.; Shekhar, Atul
作者单位：Indian Statistical Institute; Indian Statistical Institute Bangalore; Technical University of Berlin
摘要：Existence of Loewner trace is revisited. We identify finite energy paths (the skeleton of Wiener measure) as natural class of regular drivers for which we find simple and natural estimates in terms of their (Cameron-Martin) norm. Secondly, now dealing with potentially rough drivers, a representation of the derivative of the (inverse of the) Loewner flow is given in terms of a rough- and then pathwise Follmer integral. Assuming the driver within a class of It-processes, an exponential martingal...
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作者：Liu, Yuan
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：It is known that a quadratic transportation-information inequality interpolates between the Talagrand's inequality and the log-Sobolev inequality (LSI for short). The aim of this paper is threefold: (1) To prove the equivalence of and the Lyapunov condition, which gives a new characterization inspired by Cattiaux et al. (Probab Theory Relat Fields 148(1-2):285-304, 2010). (2) To prove the stability of under bounded perturbations, which gives a transference principle in the sense of Holley-Stro...
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作者：Croydon, David A.; Muirhead, Stephen
作者单位：University of Warwick; University of London; University College London; University of Oxford
摘要：We consider the quenched localisation of the Bouchaud trap model on the positive integers in the case that the trap distribution has a slowly varying tail at infinity. Our main result is that for each there exists a slowly varying tail such that quenched localisation occurs on exactly N sites. As far as we are aware, this is the first example of a model in which the exact number of localisation sites are able to be 'tuned' according to the model parameters. Key intuition for this result is pro...
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作者：[Anonymous]
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作者：Beltran, J.; Jara, M.; Landim, C.
作者单位：Pontificia Universidad Catolica del Peru; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We prove uniqueness of a martingale problem with boundary conditions on a simplex associated to a differential operator with an unbounded drift. We show that the solution of the martingale problem remains absorbed at the boundary once it attains it, and that, after hitting the boundary, it performs a diffusion on a lower dimensional simplex, similar to the original one. We also prove that in the diffusive time scale condensing zero-range processes evolve as this absorbed diffusion.
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作者：Le Gouic, Thibaut; Loubes, Jean-Michel
作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：Based on the Fr,chet mean, we define a notion of barycenter corresponding to a usual notion of statistical mean. We prove the existence of Wasserstein barycenters of random probabilities defined on a geodesic space (E, d). We also prove the consistency of this barycenter in a general setting, that includes taking barycenters of empirical versions of the probability measures or of a growing set of probability measures.
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作者：Bartholdi, Laurent; Erschler, Anna
作者单位：Universite PSL; Ecole Normale Superieure (ENS); University of Gottingen
摘要：We study the Poisson-Furstenberg boundary of random walks on permutational wreath products. We give a sufficient condition for a group to admit a symmetric measure of finite first moment with non-trivial boundary, and show that this criterion is useful to establish exponential word growth of groups. We construct groups of exponential growth such that all finitely supported (not necessarily symmetric, possibly degenerate) random walks on these groups have trivial boundary. This gives a negative...
