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作者：Gwynne, Ewain; Holden, Nina; Sun, Xin
作者单位：Massachusetts Institute of Technology (MIT); Columbia University
摘要：Let (0,2) and let h be the random distribution on C which describes a -Liouville quantum gravity (LQG) cone. Also let =16/2>4 and let be a whole-plane space-filling SLE curve sampled independent from h and parametrized by -quantum mass with respect to h. We study a family {GE}E>0 of planar maps associated with (h,) called the LQG structure graphs (a.k.a. mated-CRT maps) which we conjecture converge in probability in the scaling limit with respect to the Gromov-Hausdorff topology to a random me...
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作者：Che, Ziliang; Landon, Benjamin
作者单位：Harvard University
摘要：We consider the local statistics of H = V * XV + U * YU where V and U are independent Haar-distributed unitary matrices, and X and Y are deterministic real diagonal matrices. In the bulk, we prove that the gap statistics and correlation functions coincide with the GUE in the limit when the matrix size N -> infinity under mild assumptions on X and certain rigidity assumptions on Y (the latter being an assumption on the convergence of the eigenvalues of Y to the quantiles of its limiting spectra...
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作者：Nestoridi, Evita
作者单位：Princeton University
摘要：This paper studies Markov chains on the chambers of real hyperplane arrangements, a model that generalizes famous examples, such as the Tsetlin library and riffle shuffles. We discuss cutoff for the Tsetlin library for general weights, and we give an exact formula for the separation distance for the hyperplane arrangement walk. We introduce lower bounds, which allow for the first time to study cutoff for hyperplane arrangement walks under certain conditions. Using similar techniques, we also p...
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作者：Gayrard, Veronique
作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：We consider Metropolis dynamics of the Random Energy Model. We prove that the classical two-time correlation function that allows one to establish aging converges almost surely to the arcsine law distribution function, as predicted in the physics literature, in the optimal domain of the time-scale and temperature parameters where this result can be expected to hold. To do this we link the two-time correlation function to a certain continuous-time clock process which, after proper rescaling, is...
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作者：Forghani, Behrang; Tiozzo, Giulio
作者单位：Bowdoin College; University of Toronto
摘要：We consider random walks on finitely or countably generated free semigroups, and identify their Poisson boundaries for classes of measures which fail to meet the classical entropy criteria, namely measures with infinite entropy or infinite logarithmic moment.
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作者：Johansson, Kurt
作者单位：Royal Institute of Technology
摘要：We study the two-time distribution in directed last passage percolation with geometric weights in the first quadrant. We compute the scaling limit and show that it is given by a contour integral of a Fredholm determinant.
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作者：Addario-Berry, Louigi
作者单位：McGill University
摘要：This work proves new probability bounds relating to the height, width, and size of Galton-Watson trees. For example, if T is any Galton-Watson tree, and H, W, and |T| are the height, width, and size of T, respectively, then H/W has sub-exponential tails and H/|T|1/2 has sub-Gaussian tails. Although our methods apply without any assumptions on the offspring distribution, when information is provided about the distribution the method can be adapted accordingly, and always seems to yield tight bo...
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作者：Cox, Alexander M. G.; Obloj, Jan; Touzi, Nizar
作者单位：University of Bath; University of Oxford; Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We provide a complete characterisation of the Root solution to the Skorokhod embedding problem (SEP) by means of an optimal stopping formulation. Our methods are purely probabilistic and the analysis relies on a tailored time-reversal argument. This approach allows us to address the long-standing question of a multiple marginals extension of the Root solution of the SEP. Our main result establishes a complete solution to the n-marginal SEP using first hitting times of barrier sets by the time-...
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作者：Epstein, Charles L.; Pop, Camelia A.
作者单位：University of Pennsylvania; University of Minnesota System; University of Minnesota Twin Cities
摘要：We provide a detailed description of the structure of the transition probabilities and of the hitting distributions on boundary components of a manifold with corners for a degenerate strong Markov process arising in population genetics. The Markov processes that we study are a generalization of the classical Wright-Fisher process. The main ingredients in our proofs are based on the analysis of the regularity properties of solutions to a forward Kolmogorov equation defined on a compact manifold...
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作者：Laslier, Benoit
作者单位：Universite Paris Cite
摘要：We show that bounded changes to the boundary of a lozenge tilings do not affect the local behaviour inside the domain. As a consequence we prove the existence of a local limit in all domains with planar boundary. The proof does not rely on any exact solvability of the model beyond its links with uniform spanning trees.
