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Random walks with unbounded memory

Grant number: 18/04764-9
Support Opportunities:Scholarships abroad - Research
Effective date (Start): September 01, 2018
Effective date (End): August 31, 2019
Field of knowledge:Physical Sciences and Mathematics - Probability and Statistics - Probability
Principal Investigator:Renato Jacob Gava
Grantee:Renato Jacob Gava
Host Investigator: Iddo Ben-Ari
Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
Research place: University of Connecticut (UCONN), United States  
Associated research grant:17/10555-0 - Stochastic modeling of interacting systems, AP.TEM


We will study the elephant random walk and other similar models that present unbounded memory and that are currently in vogue in statistical physics in order to establish limit theorems. For physicists, the interest in this type of model consists in the fact that they exhibit anomalous diffusion. In addition, we will investigate open questions related to the Bak-Sneppen evolutionary model, a model that, like the random walks with unbounded memory, has received much attention of the theoretical physics community, but still with few rigorous results from the mathematical point of view.

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
COLETTI, CRISTIAN F.; DE LIMA, LUCAS R.; GAVA, RENATO J.; LUIZ, DENIS A.. Limit theorems for a random walk with memory perturbed by a dynamical system. Journal of Mathematical Physics, v. 61, n. 10, . (19/19056-2, 17/10555-0, 18/04764-9)
GAVA, RENATO J.; REZENDE, BRUNA L. F.. Some limit theorems for dependent Bernoulli random variables. Statistics & Probability Letters, v. 170, . (18/04764-9, 17/10555-0)
COLETTI, CRISTIAN F.; GAVA, RENATO J.; DE LIMA, LUCAS R.. Limit theorems for a minimal random walk model. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, . (17/10555-0, 18/04764-9)

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