Il 28 maggio alle ore 14 in Aula di Consiglio del Dipartimento di Matematica, Sapienza Università di Roma di terrà il seguente seminario di Probabilità e Statistica Matematica:

GERARD LETAC, IMT, Université Paul Sabatier, Toulouse, France

MULTIVARIATE RECIPROCAL INVERSE GAUSSIAN DISTRIBUTIONS: THE SURPRISING INTEGRALS OF SUPERSYMMETRY

Abstract If $W=(w_{ij})_{1\leq i,j\leq n})$ is a symmetric matrix with $w_{ij}\geq 0$ and zero diagonal, consider the matrix $M_x=2\mathrm{diag}(x_1,\ldots,x_n)-W$ and the set $C_W$ of $x\in \mathbb{R}^n$ such that $M_x$ is positive definite. Physicists and probabilists have considered in the last ten years several integrals equivalent to $\int_{C_W}\exp(-a^*M_xa-b^*M_x^{-1}b)(\det M_x)^{q-1}dx$. According to the properties of the undirected graph $G$ associated to $W$ with vertices $1,\ldots,n$ and edges $(i,j)$ such that $w_{ij}\neq 0$, we compute some of these integrals and we study the corresponding exponential families on $\mathbb{R}^n$ with many attractive properties.