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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
Léa Gohier, Emmanuel Humbert, Kilian Raschel
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…