## International Conference on $p$-ADIC MATHEMATICAL PHYSICS AND ITS APPLICATIONS $p$-ADICS.2015, 07-12.09.2015, Belgrade, Serbia

Sergei Nechaev

### Native ultrametricity of sparse random systems

Abstract

We demonstrate the emergence of a regular hierarchical (ultrametric) behavior of eigenvalue density in ensembles of large sparse and tridiagonal random matrices. We conjecture that ultrametricity is inherit to large systems with extremal sparse statistics and speculate about possible number-theoretic origin of ultrametricity in these systems.