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作者：Andres, Sebastian; Deuschel, Jean-Dominique; Slowik, Martin
作者单位：University of Bonn; Technical University of Berlin
摘要：We study a continuous time random walk, X, on Z(d) in an environment of random conductances taking values in (0, infinity). We assume that the law of the conductances is ergodic with respect to space shifts. We prove a quenched invariance principle for X under some moment conditions of the environment. The key result on the sublinearity of the corrector is obtained by Moser's iteration scheme.
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作者：Chen, Zhen-Qing; Croydon, David A.; Kumagai, Takashi
作者单位：University of Washington; University of Washington Seattle; University of Warwick; Kyoto University
摘要：Via a Dirichlet form extension theorem and making full use of two-sided heat kernel estimates, we establish quenched invariance principles for random walks in random environments with a boundary. In particular, we prove that the random walk on a supercritical percolation cluster or among random conductances bounded uniformly from below in a half-space, quarter-space, etc., converges when rescaled diffusively to a reflecting Brownian motion, which has been one of the important open problems in ...
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作者：Georgii, Hans-Otto; Schreiber, Tomasz; Thaele, Christoph
作者单位：University of Munich; Nicolaus Copernicus University; Ruhr University Bochum
摘要：A branching random tessellation (BRT) is a stochastic process that transforms a coarse initial tessellation of R-d into a finer tessellation by means of random cell divisions in continuous time. This concept generalises the so-called STIT tessellations, for which all cells split up independently of each other. Here, we allow the cells to interact, in that the division rule for each cell may depend on the structure of the surrounding tessellation. Moreover, we consider coloured tessellations, f...
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作者：Ameur, Yacin; Hedenmalm, Haakan; Makarov, Nikolai
作者单位：Lund University; Royal Institute of Technology; California Institute of Technology
摘要：We consider the random normal matrix ensemble associated with a potential in the plane of sufficient growth near infinity. It is known that asymptotically as the order of the random matrix increases indefinitely, the eigenvalues approach a certain equilibrium density, given in terms of Frostman's solution to the minimum energy problem of weighted logarithmic potential theory. At a finer scale, we may consider fluctuations of eigenvalues about the equilibrium. In the present paper, we give the ...
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作者：Fulman, Jason; Goldstein, Larry
作者单位：University of Southern California
摘要：With Q(q,n) the distribution of n minus the rank of a matrix chosen uniformly from the collection of all n x (n + m) matrices over the finite field F-q of size q >= 2, and Q(q) the distributional limit of Q(q,n) as n -> infinity, we apply Stein's method to prove the total variation bound 1/8q(n+m+1) <= parallel to Q(q,n) - Qq parallel to TV <= 3/q(n+m+1). In addition, we obtain similar sharp results for the rank distributions of symmetric, symmetric with zero diagonal, skew symmetric, skew cen...
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作者：Limic, Vlada; Talarczyk, Anna
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Warsaw
摘要：Consider a standard Lambda-coalescent that comes down from infinity. Such a coalescent starts from a configuration consisting of infinitely many blocks at time 0, but its number of blocks N-t is a finite random variable at each positive time t. Berestycki et al. [Ann. Probab. 38 (2010) 207-233] found the first-order approximation v for the process N at small times. This is a deterministic function satisfying N-t/v(t) -> 1 as t -> 0. The present paper reports on the first progress in the study ...
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作者：Lam, Thomas
作者单位：University of Michigan System; University of Michigan
摘要：Let W be a finite Weyl group and (W) over cap be the corresponding affine Weyl group. We show that a large element in (W) over cap, randomly generated by (reduced) multiplication by simple generators, almost surely has one of vertical bar W vertical bar-specific shapes. Equivalently, a reduced random walk in the regions of the affine Coxeter arrangement asymptotically approaches one of vertical bar W vertical bar-many directions. The coordinates of this direction, together with the probabiliti...
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作者：Mussel, Elchanan; Neeman, Joe
作者单位：University of California System; University of California Berkeley
摘要：We prove the first robust dimension free isoperimetric result for the standard Gaussian measure gamma n and the corresponding boundary measure gamma n(+) in R-n. The main result in the theory of Gaussian isoperimetry (proven in the 1970s by Sudakov and Tsirelson, and independently by Borell) states that if gamma n (A) = 1/2 then the surface area of A is bounded by the surface area of a half-space with the same measure, gamma n(+) (A) <= (2 pi)(-1/2). Our results imply in particular that if A s...
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作者：Broutin, Nicolas; Sulzbach, Henning
作者单位：McGill University
摘要：In the recursive lamination of the disk, one tries to add chords one after another at random; a chord is kept and inserted if it does not intersect any of the previously inserted ones. Curien and Le Gall [Ann. Probab. 39 (2011) 2224-2270] have proved that the set of chords converges to a limit triangulation of the disk encoded by a continuous process M. Based on a new approach resembling ideas from the so-called contraction method in function spaces, we prove that, when properly rescaled, the ...
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作者：Hammond, Alan; Pete, Gabor; Schramm, Oded
作者单位：University of Oxford; Budapest University of Technology & Economics
摘要：In dynamical critical site percolation on the triangular lattice or bond percolation on Z(2), we define and study a local time measure on the exceptional times at which the origin is in an infinite cluster. We show that at a typical time with respect to this measure, the percolation configuration has the law of Kesten's incipient infinite cluster. In the most technical result of this paper, we show that, on the other hand, at the first exceptional time, the law of the configuration is differen...
