High entropy measures on the space of lattices with escape of mass

2024/03/25 by Taehyeong Kim, Kim, Taehyeong
Economics, Econometrics and Finance · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Stochastic processes and financial applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2403.16840

openalex publication_date 2024/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any diagonal element a with two eigenvalues, we construct a sequence of a-invariant probability measures on the space of unimodular lattices with high entropy but converging to the zero measure. This extends the result of Kadyrov [Ergodic Theory Dynam. Systems, 32(1) (2012)].

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