Work

Infinite-variation Lévy processes are either strongly eroded or abrupt

Year: 2026

Type: preprint

Abstract: We prove that every real Lévy process of infinite variation is either abrupt or strongly eroded, resolving the conjectured geometric dichotomy on the smoothness of the convex hull of the graph of a Lévy path [Ann. Inst. H. Poincaré Probab. Stat. 60(4) (2024), 2352-2381]. We give counterexamples to the stronger point-hitting conjecture of Vigon. As applications, we classify convex-hull smoothness, Lipschitz-minorant contact sets and Burgers shock geometry.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.20916

Authors: Cázares, Jorge González, Kramer-Bang, David, Mijatović, Aleksandar

Institutions: Universidad Nacional Autónoma de México, Aarhus University, University of Warwick, The Alan Turing Institute

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Engineering and Physical Sciences Research Council

Awards: Anomalous diffusion via self-interaction and reflection, DMS-EPSRC: Fast martingales, large deviations and randomised gradients for heavy-tailed target distributions

OpenAlex ID: W7222620977

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