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作者：Panagiotou, Konstantinos; Stufler, Benedikt; Weller, Kerstin
作者单位：University of Munich; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We study the uniform random graph C-n with n vertices drawn from a subcritical class of connected graphs. Our main result is that the resealed graph C-n / root n converges to the Brownian continuum random tree T-e multiplied by a constant scaling factor that depends on the class under consideration. In addition, we provide sub-Gaussian tail bounds for the diameter D (C-n) and height H(C-n(center dot)) of the rooted random graph C-n(center dot) We give analytic expressions for the scaling facto...
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作者：Berard, Jean; Ramirez, Alejandro
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Pontificia Universidad Catolica de Chile
摘要：We study the following microscopic model of infection or epidemic reaction: red and blue particles perform independent nearest-neighbor continuous-time symmetric random walks on the integer lattice Z with jump rates D-R for red particles and D-B for blue particles, the interaction rule being that blue particles turn red upon contact with a red particle. The initial condition consists of i.i.d. Poisson particle numbers at each site, with particles at the left of the origin being red, while part...
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作者：Lupu, Titus
作者单位：Universite Paris Saclay
摘要：It was shown by Le Jan that the occupation field of a Poisson ensemble of Markov loops (loop soup) of parameter 1/2 associated to a transient symmetric Markov jump process on a network is half the square of the Gaussian free field. We construct a coupling between these loops and the free field such that an additional constraint holds: the sign of the free field is constant on each cluster of loops. As a consequence of our coupling we deduce that the loop clusters of parameter 1/2 do not percol...
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作者：Carmona, Philippe; Gia Bao Nguyen; Petrelis, Nicolas
作者单位：Nantes Universite; Universidad de Chile
摘要：In this paper, we investigate a model for a 1 1 dimensional self interacting and partially directed self-avoiding walk, usually referred to by the acronym IPDSAW. The interaction intensity and the free energy of the system are denoted by beta and f, respectively. The IPDSAW is known to undergo a collapse transition at beta(c). We provide the precise asymptotic of the free energy close to criticality, that is, we show that f (beta(c) - epsilon) similar to gamma epsilon(3/2) where gamma is compu...
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作者：Paulin, Daniel; Mackey, Lester; Tropp, Joel A.
作者单位：National University of Singapore; Stanford University; California Institute of Technology
摘要：This paper establishes new concentration inequalities for random matrices constructed from independent random variables. These results are analogous with the generalized Efron-Stein inequalities developed by Boucheron et al. The proofs rely on the method of exchangeable pairs.
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作者：Fyodorov, Y. V.; Khoruzhenko, B. A.; Simm, N. J.
作者单位：University of London; Queen Mary University London
摘要：The goal of this paper is to establish a relation between characteristic polynomials of N x N GUE random matrices H as N ->infinity, and Gaussian processes with logarithmic correlations. We introduce a regularized version of fractional Brownian motion with zero Hurst index, which is a Gaussian process with stationary increments and logarithmic increment structure. Then we prove that this process appears as a limit of D-N(Z) = -log vertical bar det(H - zI) on mesoscopic scales as N -> infinity....
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作者：Abert, Miklos; Glasner, Yair; Virag, Balint
作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Ben-Gurion University of the Negev; University of Toronto; University of Toronto
摘要：We give an explicit bound on the spectral radius in terms of the densities of short cycles in finite d-regular graphs. It follows that the a finite d-regular Ramanujan graph G contains a negligible number of cycles of size less than c log log vertical bar G vertical bar. We prove that infinite d-regular Ramanujan unimodular random graphs are trees. Through Benjamini-Schramm convergence this leads to the following rigidity result. If most eigenvalues of a d-regular finite graph G fall in the Al...
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作者：Blath, Jochen; Hammer, Matthias; Ortgiese, Marcel
作者单位：Technical University of Berlin; University of Munster
摘要：The continuous-space symbiotic branching model describes the evolution of two interacting populations that can reproduce locally only in the simultaneous presence of each other. If started with complementary Heaviside initial conditions, the interface where both populations coexist remains compact. Together with a diffusive scaling property, this suggests the presence of an interesting scaling limit. Indeed, in the present paper, we show weak convergence of the diffusively rescaled populations...
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作者：Liechty, Karl; Wang, Dong
作者单位：DePaul University; National University of Singapore
摘要：We consider an ensemble of n nonintersecting Brownian particles on the unit circle with diffusion parameter n(-1/2), which are conditioned to begin at the same point and to return to that point after time T, but otherwise not to intersect. There is a critical value of T which separates the subcritical case, in which it is vanishingly unlikely that the particles wrap around the circle, and the supercritical case, in which particles may wrap around the circle. In this paper, we show that in the ...
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作者：Avena, Luca; Bolthausen, Erwin; Ritzmann, Christine
作者单位：Leiden University; Leiden University - Excl LUMC; University of Zurich
摘要：We prove error bounds in a central limit theorem for solutions of certain convolution equations. The main motivation for investigating these equations stems from applications to lace expansions, in particular to weakly self-avoiding random walks in high dimensions. As an application we treat such self-avoiding walks in continuous space. The bounds obtained are sharper than those obtained by other methods.
