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Key words: Random matrices, eigenvalues, Laguerre ensemble, Wishart ensemble, bulk scaling limit.. AMS 2000 Subject Classification: Primary 60B20; Secondary:
The authors prove that for large class of random Hamiltonians the point process of properly normalized energies restricted to a sparse enough random subset of spin configuration
In particular, we prove a strong approximation result for such a random walk which, in turn, enables us to establish strong limit theorems, like the joint Strassen type law of
Keywords: Hydrodynamic scaling limit, Ulam’s problem, Hammersley’s process nonlinear conservation law, the Burgers equation, the Lax formula.. Address: Department of Mathematics,
The main result of this paper is the following local limit theorem for the joint distribution of the vector ( |C1| ,. , |C k | ) in the Erd˝ os-Rényi random graph:.. Theorem 1.1
Keywords: Brownian motion, random time change, exit boundary, local time, additive func- tional, stochastic differential equation, Khas’minskii’s lemma, spectrally negative
In Section 5.3 we make a cut-off for small times, showing that these times are negligible in the limit as κ → ∞ , perform a space-time scaling and compactification of the
Zeitouni, Limit theorems for one- dimensional transient random walks in Markov environments, to appear in Ann. Solomon, Random walks in random
