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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：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：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.
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作者：Cabezas, M.; Rolla, L. T.; Sidoravicius, V.
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA); Pontificia Universidad Catolica de Chile; University of Buenos Aires; New York University; NYU Shanghai; New York University
摘要：We study an infinite system of moving particles, where each particle is of type A or B. Particles perform independent random walks at rates D-A > 0 and D-B >= 0, and the interaction is given by mutual annihilation A + B -> empty set. The initial condition is i.i.d. with finite first moment. We show that this system is site-recurrent, that is, each site is visited infinitely many times. We also generalize a lower bound on the density decay of Bramson and Lebowitz by considering a construction t...
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作者：Richier, Loic
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We discuss asymptotics for the boundary of critical Boltzmann planar maps under the assumption that the distribution of the degree of a typical face is in the domain of attraction of a stable distribution with parameter it has a component homeomorphic to the half-plane. As an application, we identify the limits of loops conditioned to be large in the rigid loop model on quadrangulations, proving thereby a conjecture of Curien and Kortchemski.
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作者：Panagiotou, Konstantinos; Stufler, Benedikt
作者单位：University of Munich; Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：Polya trees are rooted trees considered up to symmetry. We establish the convergence of large uniform random Polya trees with arbitrary degree restrictions to Aldous' Continuum Random Tree with respect to the Gromov-Hausdorff metric. Our proof is short and elementary, and it is based on a novel decomposition: it shows that the global shape of a random Polya tree is essentially dictated by a large Galton-Watson tree that it contains. We also derive sub-Gaussian tail bounds for both the height a...
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作者：Lupu, Titus; Werner, Wendelin
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We further investigate properties of the Gaussian free field (GFF) on the metric graph associated to a discrete weighted graph (where the edges of the latter are replaced by continuous line-segments of appropriate length) that has been introduced by the first author. On such a metric graph, the GFF is a random continuous function that generalises one-dimensional Brownian bridges so that one-dimensional techniques can be used. In the present paper, we define and study the pseudo-metric defined ...
