A new exponential family related to the Vertex Reinforced Jump Process
Christophe Sabot, Pierre Tarrès, Xiaolin Zeng · arXiv (Cornell University) · 2015
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 random potential of a Schr\odinger operator, this exponential family is related to the random field that gives the mixing measure of the Vertex Reinforced Jump Process, and hence to the mixing measure of the Edge Reinforced Random Walk, the so-called magic formula. In particular, it gives by direct computation the value of the normalizing constants of these mixing measures, answering a question raised by Diaconis.