The connection between evolution algebras, random walks and graphs

ABSTRACT: Evolution algebras are a new type of non-associative algebras which are inspired from biological phenomena. A special class of such algebras, called Markov evolution algebras, is strongly related to the theory of discrete time Markov chains. The winning of this relation is that many results coming from Probability Theory may be stated in the context of Abstract Algebra. In this paper we explore the connection between evolution algebras, random walks and graphs. More precisely, we study the relationships between the evolution algebra induced by a random walk on a graph and the evolution algebra determined by the same graph. Given that any Markov chain may be seen as a random walk on a graph we believe that our results may add a new landscape in the study of Markov evolution algebras.

• Autores: Rodiño Montoya, Mary Luz; Cadavid Salazar, Paula Andrea; Rodríguez, Pablo Martín
• Tipo de recurso: Article of investigation
• Fecha de publicación: 2018
• Institución: Universidad de Antioquia
• Repositorio: Repositorio UdeA
• Idioma: eng
• OAI Identifier: oai:bibliotecadigital.udea.edu.co:10495/37304
• Acceso en línea: https://hdl.handle.net/10495/37304
• Palabra clave: Álgebra; Algebra; Álgebra - métodos gráficos; Algebra - Graphic methods; Ecuaciones de evolución; Evolution equations; Teoría de grafos; Graph theory
• Rights: openAccess
• License: http://creativecommons.org/licenses/by/2.5/co/