Marches al\'eatoires dans un c\^one et fonctions discr\`etes harmoniques

Kilian Raschel; Pierre Tarrago

Marches al\'eatoires dans un c\^one et fonctions discr\`etes harmoniques

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arxiv 2211.02925 v1 pith:ENOBWJK2 submitted 2022-11-05 math.PR math.CO

Kilian Raschel , Pierre Tarrago This is my paper · ORCID

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Random walks in cones have the double interest of being at the heart of many probabilistic problems and of being related to many mathematical fields, such as spectral theory, combinatorics, or discrete complex analysis. In this article, we present some key ideas associated with these processes: we will discuss their definition, the link with Brownian motion in cones, as well as some recent research topics such as the construction of discrete harmonic functions.

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Axis-Driven Random Walks on $\mathbb{Z}^2$ (transient cases)
math.PR 2024-11 conditional novelty 6.0 of 10

For any repulsion strength alpha below 1/2, an axis-driven random walk on the first quadrant is transient and superdiffusive, with distance scaling like n^(1/(2(1-alpha))).

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