Two repelling random walks on Z

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Author(s):	Prado, Fernando P. A. ; Coletti, Cristian F. ; Rosales, Rafael A. Total Authors: 3
Document type:	Journal article
Source:	Stochastic Processes and their Applications; v. 160, p. 17-pg., 2023-03-06.
Abstract
We consider two interacting random walks on Z such that the transition probability of one walk in one direction decreases exponentially with the number of transitions of the other walk in that direction. The joint process may thus be seen as two random walks reinforced to repel each other. The strength of the repulsion is further modulated in our model by a parameter beta >= 0. When beta = 0 both processes are independent symmetric random walks on Z, and hence recurrent. We show that both random walks are further recurrent if beta is an element of(0, 1]. We also show that these processes are transient and diverge in opposite directions if beta > 2. The case beta is an element of(1, 2] remains widely open. Our results are obtained by considering the dynamical system approach to stochastic approximations. (c) 2023 Elsevier B.V. All rights reserved. (AU)

FAPESP's process:	17/10555-0 - Stochastic modeling of interacting systems
Grantee:	Fabio Prates Machado
Support Opportunities:	Research Projects - Thematic Grants


FAPESP's process:	11/51509-5 - Externalities and economic behavior
Grantee:	Fernando Pigeard de Almeida Prado
Support Opportunities:	Regular Research Grants