Related papers: Another probabilistic construction of ${\Phi}^{2n}…
In this paper, we present a probabilistic extension of the Fubini polynomials and numbers associated with a random variable satisfying some appropriate moment conditions. We obtain the exponential generating function and an integral…
We study a new two-dimensional quantum gravity theory, based on a gravitational action containing both the familiar Liouville term and the Mabuchi functional, which has been shown to be related to the coupling of non-conformal matter to…
This note discusses the higher K-energy functionals which were defined by Bando and Mabuchi, and integrate higher Futaki invariants. Two new formulas for the higher K-energy functionals are given, and the second K-energy is shown to be…
In previous works in this series we focussed on Hamiltonian renormalisation of free field theories in all spacetime dimensions. In this paper we address the Hamiltonian renormalisation of the self-interacting scalar field in two spacetime…
A variational method is discussed, extending the Gaussian effective potential to higher orders. The single variational parameter is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the…
We summarise recent results for the chiral Random Two-Matrix Theory constructed to describe QCD in the epsilon-regime with imaginary chemical potential. The virtue of this theory is that unquenched Lattice simulations can be used to…
We consider potential theory on Bratteli diagrams arising from Macdonald polynomials. The case of Hall-Littlewood polynomials is particularly interesting; the elements of the diagram are partitions, the branching multiplicities are…
We determine the leading order of the maximum of the random potential associated to a two-dimensional Coulomb gas for general $\beta$ and general confinement potential, extending the recent result of Lambert-Lebl\'e-Zeitouni. In the case…
We extend results of Zeitouni-Zelditch on large deviations principles for zeros of Gaussian random polynomials $s$ in one complex variable to certain non-Gaussian ensembles that we call $P(\phi)_2$ random polynomials. The probability…
Multivariate versions of classical orthogonal polynomials such as Jacobi, Hahn, Laguerre and Meixner are reviewed and their connection explored by adopting a probabilistic approach. Hahn and Meixner polynomials are interpreted as posterior…
The Mabuchi energy is an interesting geometric functional on the space of K\"ahler metrics that plays a crucial r\^ole in the study of the geometry of K\"ahler manifolds. We show that this functional, as well as other related geometric…
This publication is an exercise which extends to two variables the Christoffel's construction of orthogonal polynomials for potentials of one variable with external sources. We generalize the construction to biorthogonal polynomials. We…
We analyze the connection between $p_T$ and multiplicity distributions in a statistical framework. We connect the Tsallis parameters, $T$ and $q$, to physical properties like average energy per particle and the second scaled factorial…
We study distributions of random vectors whose components are second order polynomials in Gaussian random variables. Assuming that the law of such a vector is not absolutely continuous with respect to Lebesgue measure, we derive some…
Inspired by the works in [1] and [8] we introduce what we call $k$-th-order fluctuation fields and study their scaling limits. This construction is done in the context of particle systems with the property of orthogonal self-duality. This…
A new set of multiple orthogonal polynomials of both type I and type II with respect to two weight functions involving Gauss' hypergeometric function on the interval $(0,1)$ is studied. This type of polynomials have direct applications in…
We consider a scalar Fermi-Pasta-Ulam (FPU) system on a square 2D lattice. The Kadomtsev-Petviashvili (KP-II) equation can be derived by means of multiple scale expansions to describe unidirectional long waves of small amplitude with slowly…
We will denote by $\mathcal{M}$ the space of Borel probabilities on the symbolic space $\Omega=\{1,2...,m\}^\mathbb{N}$. $\mathcal{M}$ is equipped Monge-Kantorovich metric. We consider here the push-forward map $\mathfrak{T}:\mathcal{M} \to…
This announcement describes a probabilistic approach to cascades which, in addition to providing an entirely probabilistic proof of the Kahane-Peyri\`ere theorem for independent cascades, readily applies to general dependent cascades.…
Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. In this paper, we study the probabilistic central Bell polynomials associated with random variable Y, as probabilistic extension of the…