Some Asymptotic and Large Deviation Results in Poisson Approximation

Some Large Deviation Results for Dynamical Systems

We prove some large deviation estimates for continuous maps of compact metric spaces and apply them to attractors in differentiable dynamics, rate of escape problems, and to shift spaces. Introduction Consider a discrete time dynamical system generated by a self-map /: X O of some domain X. Let m be a reference measure on X, and let <p : X —► R be an observable. Suppose that £ J2"fx <p ° f conv...

Some large deviation results for sparse random graphs

We obtain a large deviation principle (LDP) for the relative size of the largest connected component in a random graph with small edge probability. The rate function, which is not convex in general, is determined explicitly using a new technique. The proof yields an asymptotic formula for the probability that the random graph is connected. We also present an LDP and related result for the numbe...

Some path large deviation results for a branching diffusion

We give an intuitive proof of a path large-deviations result for a typed branching diffusion as found in Git, J.Harris and S.C.Harris [4]. Our approach involves an application of a change of measure technique involving a distinguished infinite line of descent, or spine, and we follow the spine setup of Hardy and Harris [5, 7, 6]. Our proof combines simple martingale ideas with applications of V...

Some Results on p-Best Approximation in Vector Spaces

Poisson point processes: large deviation inequalities for the convex distance

An analogue of Talagrand’s convex distance for binomial and Poisson point processes is defined. A corresponding large deviation inequality is proved.