Alexsandro Giacomo Grimbert Gallo in research grants and scholarships supported by FAPESP.
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The project splits essentially into the study of two random objects. 1- Concerning stochastic chains with unbounded memory, we will continue the researches initiated since my PhD, increasing some new topics of interest. In a generic way, we want to obtain global characterisations of the measures (stationary or not), starting from the knowledge of local rules of interaction. We will focus …
We propose to develop a general study of long range stochastic chains, under several approaches listed below.(1) Questions related to existence and uniqueness of the stationary measure. (2) Construction of algorithms that perfectly simulates the stationary measure, and relation with the notion of finitary coding. (3) Relation between the notion of Gibbsianess and the notion of regularity …
Clementi et al.(2016) introduced an information spreading model over a sequence of (Markovian) random graphs. Our ultimate goal is to provide an alternative proof based on the concept of strong stationary times. An initial, and important, part of the project will be dedicated to a preliminary study of phase transition phenomenons in random graphs and strong stationary times theory for Mar…
The main objective of this project is to understand how the phase transition phenomenon is analizes in statistical physics, that is, using probability theory and stochastic processes. For that, we plan to study two well-known and studied spin models, the Curie-Weiss (mean field) model and the Ising model in two dimensions. Besides this study, which involves concepts going beyond the basic…
In this project, the student will study all the necessary concepts to establish the cutoff phenomenon for Markov chains with finite state space. He will focus on some cards shuffling, like top-to-random shuffle, riffle shuffle, among others. This will be the opportunity to make a bridge between classical topics seen during the undergraduate course, and some more refined concepts which are…
Stochastic chains with unbounded memory are a natural generalization of Markov chains, in the sense that the transition probabilities may depend on the whole past. These process, introduced by Onicescu and Mihoc (1935) and Doeblin and Fortet (1937), have been receiving increasing attention in the probabilistic literature, because they form a class richer than the Markov chains and have pr…
This project contains two principal parts which can be seen as a continuation and generalization of the PhD Thesis of the candidate. First, we will use the regenerative structure of the stochastic processes with unbounded variable length memory which have been introduced in the PhD Thesis \citep{gallo/2009} to solve two questions of actual probability theory. The first one is the Monge-Ka…
The main objective of the present project is to study the Poincaré recurrence statistics, and their relations with extreme value theory, for stochastic processes (or equivalently, dynamical systems). Our focus will be through a statistics of the process called first possible return time. First, we want to study the asymptotic properties of the first possible return time, under general co…
| 2 / 2 | Completed research grants |
| 2 / 2 | Ongoing scholarships in Brazil |
| 4 / 3 | Completed scholarships in Brazil |
| 1 / 1 | Completed scholarships abroad |
| 9 / 8 | All research grants and scholarships |
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