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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...
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作者：Armendariz, Ines; Grosskinsky, Stefan; Loulakis, Michail
作者单位：University of Buenos Aires; University of Warwick; National Technical University of Athens
摘要：Zero-range processes with decreasing jump rates are known to exhibit condensation, where a finite fraction of all particles concentrates on a single lattice site when the total density exceeds a critical value. We study such a process on a one-dimensional lattice with periodic boundary conditions in the thermodynamic limit with fixed, super-critical particle density. We show that the process exhibits metastability with respect to the condensate location, i.e. the suitably accelerated process o...
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作者：Knowles, Antti; Yin, Jun
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Wisconsin System; University of Wisconsin Madison
摘要：We develop a new method for deriving local laws for a large class of random matrices. It is applicable to many matrix models built from sums and products of deterministic or independent random matrices. In particular, it may be used to obtain local laws for matrix ensembles that are anisotropic in the sense that their resolvents are well approximated by deterministic matrices that are not multiples of the identity. For definiteness, we present the method for sample covariance matrices of the f...
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作者：Chen, Wei-Kuo; Dey, Partha; Panchenko, Dmitry
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Illinois System; University of Illinois Urbana-Champaign; University of Toronto
摘要：We show that the free energy in the mixed p-spin models of spin glasses does not superconcentrate in the presence of external field, which means that its variance is of the order suggested by the Poincar, inequality. This complements the result of Chatterjee who showed that the free energy superconcentrates when there is no external field. For models without odd p-spin interactions for , we prove the central limit theorem for the free energy at any temperature and give an explicit formula for ...
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作者：Duhalde, Xan; Duquesne, Thomas
作者单位：Sorbonne Universite
摘要：We consider super processes whose spatial motion is the d-dimensional Brownian motion and whose branching mechanism is critical or subcritical; such processes are called -super Brownian motions. If , where is the lower index of at , then the total range of the -super Brownian motion has an exact packing measure whose gauge function is , where . More precisely, we show that the occupation measure of the -super Brownian motion is the g-packing measure restricted to its total range, up to a deter...
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作者：Dahmer, Iulia; Kersting, Goetz
作者单位：Goethe University Frankfurt
摘要：The evolving Kingman coalescent is the tree-valued process which records the time evolution undergone by the genealogies of Moran populations. We consider the associated process of total external tree length of the evolving Kingman coalescent and its asymptotic behaviour when the number of leaves of the tree tends to infinity. We show that on the time-scale of the Moran model slowed down by a factor equal to the population size, the (centred and rescaled) external length process converges to a...
