We study right tail large deviations of the logarithm of the partition function for directed lattice paths in i.i.d. random potentials. The main purpose is the derivation of explicit formulas for the 1+1-dimensional exactly solvable case with log-gamma distributed random weights. Along the way we establish some regularity results for this rate function for general distributions in arbitrary dim...

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We give an explicit formula for the mean square displacement of random walk on d -dimensional Manhattan lattice after n steps, all and dimensions ≥ 2 .

Given any fixed N×N positive semi-definite diagonal matrix G ≥ 0 we derive the explicit formula for the density of complex eigenvalues for random matrices A of the form A = U √ G where the random unitary matrices U are distributed on the group U(N) according to the Haar measure.

This paper states a law of large numbers for a random walk in a random iid environment on Z, where the environment follows some Dirichlet distribution. Moreover, we give explicit bounds for the asymptotic velocity of the process and also an asymptotic expansion of this velocity at low disorder

Large deviation principles and related results are given for a class of Markov chains associated to the “leaves” in random recursive trees and preferential attachment random graphs, as well as the “cherries” in Yule trees. In particular, the method of proof, combining analytic and Dupuis-Ellis type path arguments, allows for an explicit computation of the large deviation pressure.

The spectral densities of the weighted Laplacian, random walk, and weighted adjacency matrices associated with a random complex network are studied using the replica method. The link weights are parametrized by a weight exponent beta. Explicit results are obtained for scale-free networks in the limit of large mean degree after the thermodynamic limit, for arbitrary degree exponent and beta.

Recently, Williams [Bull. London Math. Soc. 34 (2002) 610–612] gave an explicit example of a random time � associated with Brownian motion such that � is not a stopping time but E(M�)=E(M0) for every bounded martingale M. The aim of this paper is to characterize such random times, which we call pseudo-stopping times, and to construct further examples, using techniques of progressive enlargement...

Although explicit and implicit knowledge of language learners are essential to theoretical and pedagogical debates in second language acquisition (SLA), little research has addressed the effects of instructional interventions on the two knowledge types (R. Ellis, 2005).This study examined the relative effectiveness of explicit and implicit types of form-focused instruction (FFI) on the acquisit...