The Vertex Reinforced Jump Process and a random Schrödinger operator on finite graphs
Sabot, Christophe; Tarrès, Pierre; Zeng, Xiaolin (2017), The Vertex Reinforced Jump Process and a random Schrödinger operator on finite graphs, Annals of Probability, 45, 6A, p. 3967 - 3986. 10.1214/16-AOP1155
View/ Open
Type
Article accepté pour publication ou publiéDate
2017Journal name
Annals of ProbabilityVolume
45Number
6APublisher
Institute of Mathematical Statistics
Pages
3967 - 3986
Publication identifier
Metadata
Show full item recordAuthor(s)
Sabot, ChristopheInstitut Camille Jordan [Villeurbanne] [ICJ]
Tarrès, Pierre
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Zeng, Xiaolin

Institut Camille Jordan [Villeurbanne] [ICJ]
Abstract (EN)
We introduce a new exponential family of probability distributions, which can be viewed as a multivariate generalization of the inverse Gaussian distribution. Considered as the potential of a random Schrödinger operator, this exponential family is related to the random field that gives the mixing measure of the Vertex Reinforced Jump Process (VRJP), and hence to the mixing measure of the Edge Reinforced Random Walk (ERRW), the so-called magic formula. In particular, it yields by direct computation the value of the normalizing constants of these mixing measures, which solves a question raised by Diaconis. The results of this paper are instrumental in [Sabot and Zeng (2015)], where several properties of the VRJP and the ERRW are proved, in particular a functional central limit theorem in transient regimes, and recurrence of the 2-dimensional ERRW.Subjects / Keywords
random Schrödinger operator; Self-interacting random walks; supersymmetric hyperbolic nonlinear sigma model; Vertex-reinforced jump processRelated items
Showing items related by title and author.
-
Sabot, Christophe; Tarres, Pierre (2015) Article accepté pour publication ou publié
-
Sabot, Christophe; Tarres, Pierre (2015) Article accepté pour publication ou publié
-
Disertori, Margherita; Sabot, Christophe; Tarres, Pierre (2015) Article accepté pour publication ou publié
-
Lupu, Titus; Sabot, Christophe; Tarrès, Pierre (2020) Article accepté pour publication ou publié
-
Lupu, Titus; Sabot, Christophe; Tarrès, Pierre (2021) Article accepté pour publication ou publié