Explicit formulae for time-space Brownian chaos

Explicit formulae for Kerov polynomials

We prove two formulae expressing the Kerov polynomial Σk as a weighted sum over the set of noncrossing partitions of the set {1, . . . , k + 1}. We also give a combinatorial description of a family of symmetric functions specializing in the coefficients of Σk .

On explicit occupation time distributions for Brownian processes

Explicit expressions for the occupation time distribution of Brownian bridge, excursion and meander are derived using Kac’s formula and results of [4]. The first two distributions appeared in [8], and were derived using weak convergence of simple random walk.

Representation formulae for the fractional Brownian motion

We discuss the relationships between some classical representations of the fractional Brownian motion, as a stochastic integral with respect to a standard Brownian motion, or as a series of functions with independent Gaussian coefficients. The basic notions of fractional calculus which are needed for the study are introduced. As an application, we also prove some properties of the Cameron-Marti...

Large-deviation approach to space-time chaos.

In this Letter, we show that the analysis of Lyapunov-exponent fluctuations contributes to deepen our understanding of high-dimensional chaos. This is achieved by introducing a gaussian approximation for the large-deviation function that quantifies the fluctuation probability. More precisely, a diffusion matrix D (a dynamical invariant itself) is measured and analyzed in terms of its principal ...

Space-Time Approach to Quantum Chaos