Recurrence and transience preservation for vertex reinforced jump processes in one dimension

Autor:	Burgess Davis, Noah Dean
Rok vydání:	2010
Předmět:	Computer Science::Machine Learning Combinatorics Discrete mathematics Vertex (graph theory) 60K37 General Mathematics Dimension (graph theory) Jump 60J10 Mathematics
Zdroj:	Illinois J. Math. 54, no. 3 (2010), 869-893
ISSN:	0019-2082
DOI:	10.1215/ijm/1336049980
Popis:	We show that the application of linear vertex reinforcement to one dimensional nearest neighbor Markov processes, yielding associated vertex reinforced jump processes, preserves both recurrence and transience. The analog for discrete time linear bond reinforcement is due to Takeshima. This together with another result we prove adds to the numerous known parallels between these two reinforcements. Martingales are the primary tool used to study vertex reinforced jump processes.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1b0e794e6645e8a2a4fb9588d0ab7d52 https://doi.org/10.1215/ijm/1336049980 Zobrazit plný text záznamu