The connection between evolution algebras, random walks and graphs

Autor(es)

Cadavid, Paula ^[1] ; Rodino Montoya, Mary Luz ^[2] ; Rodriguez, Pablo M. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Av Trabalhador Sao Carlense 400, BR-13560970 Sao Carlos, SP - Brazil

^[2] Univ Antioquia, Inst Matemat, Calle 67 53-108, Medellin - Colombia

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF ALGEBRA AND ITS APPLICATIONS; v. 19, n. 2 FEB 2020.
• Citações Web of Science: 3

Resumo

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. (AU)

• Processo FAPESP: 15/03868-7 - Comportamento assintótico de processos estocásticos em grafos e aplicações
• Beneficiário: Pablo Martin Rodriguez
• Modalidade de apoio: Bolsas no Exterior - Pesquisa