2015/07/16 by Christophe Sabot, Sabot, Christophe, Pierre Tarrès +3 · 2 citations
Computer Science · Mathematics · #60K35 #60K37 (Primary) #81T25 #81T60 (Secondary) #82B44 #Bayesian Methods and Mixture Models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1507.04660
openalex publication_date 2015/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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-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.