Walks on groups, counting reducible matrices, polynomials, and surface and free group automorphisms

DOI10.1215/00127094-2008-009zbMath1207.20068arXivmath/0703532OpenAlexW2070840198WikidataQ56907157 ScholiaQ56907157MaRDI QIDQ2482870

Igor Rivin

Publication date: 25 April 2008

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0703532

zbMATH Keywords

Galois groupssemisimple Lie groupsmapping class groupsfree group automorphismsrandom walks on graphslinear groupscompact groupsrandom products of matrices

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Semisimple Lie groups and their representations (22E46) Automorphisms of infinite groups (20E36) Linear algebraic groups over global fields and their integers (20G30) General geometric structures on low-dimensional manifolds (57M50) Arithmetic algebraic geometry (Diophantine geometry) (11G99) Free nonabelian groups (20E05) Probabilistic methods in group theory (20P05)

Related Items (48)

Towards van der Waerden’s conjecture ⋮ Random equations in free groups ⋮ Random methods in 3-manifold theory ⋮ Computing the geometric endomorphism ring of a genus-2 Jacobian ⋮ Contracting elements and random walks ⋮ Random walks on weakly hyperbolic groups ⋮ Sieve methods in group theory I: Powers in linear groups ⋮ On the genericity of loxodromic actions ⋮ A train track directed random walk on Out(F_r) ⋮ Equivariant Euler characteristics of symplectic buildings ⋮ Dynamics on free-by-cyclic groups ⋮ Counting problems in graph products and relatively hyperbolic groups ⋮ Semiclassical measures for higher-dimensional quantum cat maps ⋮ Taking the high-edge route of rank-3 outer space ⋮ Random walks on mapping class groups ⋮ Random walks on the mapping class group ⋮ Random equations in nilpotent groups. ⋮ The geometry of purely loxodromic subgroups of right-angled Artin groups ⋮ Sieve methods in group theory. II: The mapping class group ⋮ Random subgroups of linear groups are free. ⋮ Transience of algebraic varieties in linear groups -- applications to generic Zariski density. ⋮ The closure of a random braid is a hyperbolic link ⋮ SIEVE METHODS IN GROUP THEORY III: Aut(F_n) ⋮ On pseudo-Anosov autoequivalences ⋮ The compression body graph has infinite diameter ⋮ Irreducibility of Random Polynomials ⋮ Linear progress in the complex of curves ⋮ Quasimorphisms, random walks, and transient subsets in countable groups ⋮ Statistics and compression of scl ⋮ Growth in free groups (and other stories) -- twelve years later ⋮ Exponentially generic subsets of groups ⋮ The minimally displaced set of an irreducible automorphism of \(F_N\) is co-compact ⋮ The stratum of random mapping classes ⋮ How to pick a random integer matrix? (and other questions) ⋮ Recurrence of quadratic differentials for harmonic measure ⋮ Compact quotients of Cahen-Wallach spaces ⋮ North–South dynamics of hyperbolic free group automorphisms on the space of currents ⋮ Genericity of contracting elements in groups ⋮ Surjectivity of Galois representations in rational families of abelian varieties ⋮ Genericity of pseudo-Anosov mapping classes, when seen as mapping classes ⋮ Expander graphs in pure and applied mathematics ⋮ ON THE DISTRIBUTION OF GALOIS GROUPS ⋮ Some counting questions for matrices with restricted entries ⋮ COMPONENTS OF RANDOM LINKS ⋮ Stable Strata of Geodesics in Outer Space ⋮ A symplectic prolegomenon ⋮ Book Review: Thurston’s work on surfaces ⋮ Random outer automorphisms of free groups: Attracting trees and their singularity structures

Cites Work

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