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作者：Kriecherbauer, Thomas; Venker, Martin
作者单位：University of Bayreuth; Universite Catholique Louvain
摘要：We study a class of interacting particle systems on R which was recently investigated by Gotze and Venker (Ann Probab 42(6): 2207-2242, 2014. doi: 10.1214/ 13-AOP844). These ensembles generalize eigenvalue ensembles of Hermitian random matrices by allowing different interactions between particles. Although these ensembles are not known to be determinantal one can use the stochastic linearization method of Gotze and Venker (Ann Probab 42(6): 2207-2242, 2014. doi: 10.1214/13-AOP844) to represent...
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作者：Hasebe, Takahiro; Huang, Hao-Wei; Wang, Jiun-Chau
作者单位：Hokkaido University; National Sun Yat Sen University; University of Saskatchewan
摘要：In this paper additive bi-free convolution is defined for general Borel probability measures, and the limiting distributions for sums of bi-free pairs of self-adjoint commuting random variables in an infinitesimal triangular array are determined. These distributions are characterized by their bi-freely infinite divisibility, and moreover, a transfer principle is established for limit theorems in classical probability theory and Voiculescu's bi-free probability theory. Complete descriptions of ...
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作者：Chen, Wei-Kuo; Handschy, Madeline; Lerman, Gilad
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We investigate the energy landscape of the mixed even p-spin model with Ising spin configurations. We show that for any given energy level between zero and the maximal energy, with overwhelming probability there exist exponentially many distinct spin configurations such that their energies stay near this energy level. Furthermore, their magnetizations and overlaps are concentrated around some fixed constants. In particular, at the level of maximal energy, we prove that the Hamiltonian exhibits...
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作者：Ahlberg, Daniel; Tassion, Vincent; Teixeira, Augusto
作者单位：Uppsala University; University of Geneva
摘要：We study the phase transition of random radii Poisson Boolean percolation: Around each point of a planar Poisson point process, we draw a disc of random radius, independently for each point. The behavior of this process is well understood when the radii are uniformly bounded from above. In this article, we investigate this process for unbounded (and possibly heavy tailed) radii distributions. Under mild assumptions on the radius distribution, we show that both the vacant and occupied sets unde...
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作者：Harper, Adam J.; Lamzouri, Youness
作者单位：University of Cambridge; University of Warwick; York University - Canada
摘要：We investigate the race between prime numbers in many residue classes modulo q, assuming the standard conjectures GRH and LI. Among our results we exhibit, for the first time, n-way prime number races modulo q where the biases do not dissolve when n, q -> infinity. We also study the leaders in the prime number race, obtaining asymptotic formulae for logarithmic densities when the number of competitors can be as large as a power of q, whereas previous methods could only allow a power of log q. ...
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作者：Bufetov, Alexander I.; Fan, Shilei; Qiu, Yanqi
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Aix-Marseille Universite; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS; HSE University (National Research University Higher School of Economics); Saint Petersburg State University; Central China Normal University; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：For a determinantal point process induced by the reproducing kernel of the weighted Bergman space A2(U,.) over a domain U. Cd, we establish the mutual absolute continuity of reduced Palm measures of any order provided that the domain U contains a non-constant bounded holomorphic function. The result holds in all dimensions. The argument uses the H 8 (U)-module structure of A2(U,.). A corollary is the quasi-invariance of our determinantal point process under the natural action of the group of c...
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作者：Conforti, Giovanni; Von Renesse, Max
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris; Leipzig University
摘要：In this paper we establish quantitative results about the bridges of the Langevin dynamics and the associated reciprocal processes. They include an equivalence between gradient estimates for bridge semigroups and couplings, comparison principles, bounds of the distance between bridges of different Langevin dynamics, and a logarithmic Sobolev inequality for bridge measures. The existence of an invariant measure for the bridges is also discussed and quantitative bounds for the convergence to the...
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作者：Adler, Robert J.; Krishnan, Sunder Ram; Taylor, Jonathan E.; Weinberger, Shmuel
作者单位：Technion Israel Institute of Technology; Stanford University; University of Chicago
摘要：Motivated by questions of manifold learning, we study a sequence of random manifolds, generated by embedding a fixed, compact manifold M into Euclidean spheres of increasing dimension via a sequence of Gaussian mappings. One of the fundamental smoothness parameters of manifold learning theorems is the reach, or critical radius, of M. Roughly speaking, the reach is a measure of a manifold's departure from convexity, which incorporates both local curvature and global topology. This paper develop...
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作者：Habermann, Karen
作者单位：University of Cambridge
摘要：We study the small-time fluctuations for diffusion processes which are conditioned by their initial and final positions, under the assumptions that the diffusivity has a sub-Riemannian structure and that the drift vector field lies in the span of the sub-Riemannian structure. In the case where the endpoints agree and the generator of the diffusion process is non-elliptic at that point, the deterministic Malliavin covariance matrix is always degenerate. We identify, after a suitable rescaling, ...
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作者：Bowditch, Adam
作者单位：University of Warwick
摘要：We study biased random walk on subcritical and supercritical Galton-Watson trees conditioned to survive in the transient, sub-ballistic regime. By considering offspring laws with infinite variance, we extend previously known results for the walk on the supercritical tree and observe new trapping phenomena for the walk on the subcritical tree which, in this case, always yield sub-ballisticity. This is contrary to the walk on the supercritical tree which always has some ballistic phase.
