Emmanuel Humbert

collaborators

5 papers

math.CO2025

On the finiteness of the group associated with weighted walks in multidimensional orthants

Andrew Elvey Price, Emmanuel Humbert, Kilian Raschel

In the study of walks with small steps confined to multidimensional orthants, a certain group of transformations plays a central role. In particular, several techniques to potentia…

math.DG2025

Extremising eigenvalues of the GJMS operators in a fixed conformal class

Emmanuel Humbert, Romain Petrides, Bruno Premoselli

Let $(M, g)$ be a closed Riemannian manifold of dimension $n \geq 3$ . If $s$ is a positive integer satisfying $2 s < n$ , we let $P_{g}^{s}$ be the GJMS operator of order $2 s$ in $M$ . We inv…

math.PR2025

Discrete harmonic polynomials in multidimensional orthants

Emmanuel Humbert, Kilian Raschel

We consider multidimensional random walks in pyramidal cones (or multidimensional orthants), which are intersections of a finite number of half-spaces. We explore the connection be…

math.PR2025

Enumeration of walks in multidimensional orthants and reflection groups

We consider (random) walks in a multidimensional orthant. Using the idea of universality in probability theory, one can associate a unique polyhedral domain to any given walk model…

math.PR2024

On the first hitting time of a high-dimensional orthant

Emmanuel Humbert, Kilian Raschel

We consider a collection of independent standard Brownian particles (or random walks), starting from a configuration where at least one particle is positive, and study the first ti…