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We prove an almost sure limit theorem on the exact convergence rate of the maximum of standardized gaussian random walk increments.. On a conjecture of R´
Key words: Brownian sheet, functional central limit theorem, Hölder space, invariance princi- ple, triangular array, summation process.. AMS 2000 Subject Classification:
Key words: Random matrices, eigenvalues, Laguerre ensemble, Wishart ensemble, bulk scaling limit.. AMS 2000 Subject Classification: Primary 60B20; Secondary:
Key words: asymptotic formula, Green function, random walk of zero mean and finite variances, absorption on a line.. AMS 2000 Subject Classification: Primary 60G50;
We prove a non-standard functional limit theorem for a two dimensional simple random walk on some randomly oriented lattices.. This random walk, already known to be transient, has
Merkl and Rolles (see [14]) studied the recurrence of the original reinforced random walk, the so-called linearly bond-reinforced random walk, on two-dimensional graphs.. Sellke
A Central Limit Theorem for non-commutative random variables is proved using the Lindeberg method.. The theorem is a generalization of the Central Limit Theorem for free random
However, the well known Grimmett–Kesten–Zhang theorem about the transience of nearest–neighbor random walk on the infinite cluster in d > 3 ([15], see also [5] for an
