Large deviations in random latin squares

Large Deviations for Random Walk in Random

Large Deviations for Random Trees.

We consider large random trees under Gibbs distributions and prove a Large Deviation Principle (LDP) for the distribution of degrees of vertices of the tree. The LDP rate function is given explicitly. An immediate consequence is a Law of Large Numbers for the distribution of vertex degrees in a large random tree. Our motivation for this study comes from the analysis of RNA secondary structures.

Large Deviations in the Random Sieve

The proportion k of gaps with length k between square-free numbers is shown to satisfy log k = 1 + o(1) (6== 2)k log k as k ! 1. Such asymptotics are consistent with Erd} os's challenge to prove that the gap following the square-free number t is smaller than c log t= log log t, for all t and some constant c satisfying c > 2 =12. The results of this paper are achieved by studying the probabiliti...

Large Deviations in Randomly Coloured Random Graphs

Models of random graphs are considered where the presence or absence of an edge depends on the random types (colours) of its vertices, so that whether or not edges are present can be dependent. The principal objective is to study large deviations in the number of edges. These graphs provide a natural example with two different non-degenerate large deviation regimes, one arising from large devia...

Averaged Large Deviations for Random Walk in a Random Environment

Abstract. In his 2003 paper, Varadhan proves the averaged large deviation principle (LDP) for the mean velocity of a particle performing random walk in a random environment (RWRE) on Z with d ≥ 1, and gives a variational formula for the corresponding rate function Ia. Under the non-nestling assumption (resp. Kalikow’s condition), we show that Ia is strictly convex and analytic on a non-empty op...