Random walks, Gaussian processes and list structures

Random Walks and Branching Processes in Correlated Gaussian Environment

We study persistence probabilities for random walks in correlated Gaussian random environment first studied by Oshanin, Rosso and Schehr [27]. From the persistence results, we can deduce properties of critical branching processes with offspring sizes geometrically distributed with correlated random parameters. More precisely, we obtain estimates on the tail distribution of its total population ...

On Dynamical Gaussian Random Walks

Motivated by the recent work of Benjamini, Häggström, Peres, and Steif (2003) on dynamical random walks, we: (i) Prove that, after a suitable normalization, the dynamical Gaussian walk converges weakly to the Ornstein–Uhlenbeck process in classical Wiener space; (ii) derive sharp tailasymptotics for the probabilities of large deviations of the said dynamical walk; and (iii) characterize (by way...

Branching Processes and Random Walks

Coarse-grained embeddings of time series: random walks, Gaussian random processes, and deterministic chaos

A new method for studying time series is described based on a statistic indicating the degree to which trajectories passing through a small region of an embedding space are parallel. The method is particularly suited to time series with a significant correlation time. Analytic results are presented for Brownian motion and Gaussian random processes. These are generally different from the results...

Random Walks on Text Structures

Since the early ages of artificial intelligence, associative or semantic networks have been proposed as representations that enable the storage of language units and the relationships that interconnect them, allowing for a variety of inference and reasoning processes, and simulating some of the functionalities of the human mind. The symbolic structures that emerge from these representations cor...