Growth in free groups (and other stories) -- twelve years later

zbMath1225.05128arXivmath/9911076MaRDI QIDQ716406

Igor Rivin

Publication date: 28 April 2011

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9911076

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Cohomology of groups (20J06) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Paths and cycles (05C38) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) (22E27) Free nonabelian groups (20E05) Trigonometric polynomials, inequalities, extremal problems (42A05)

Related Items (16)

Conjugacy languages in groups ⋮ Central limit theorems for counting measures in coarse negative curvature ⋮ On the asymptotics of visible elements and homogeneous equations in surface groups. ⋮ Formal conjugacy growth in graph products. I ⋮ The conjugacy growth of the soluble Baumslag-Solitar groups ⋮ Counting conjugacy classes in groups with contracting elements ⋮ Conjugacy growth of commutators ⋮ Statistics in conjugacy classes in free groups ⋮ Conjugacy growth series and languages in groups ⋮ Symmetrized Chebyshev polynomials ⋮ Linking numbers of modular knots ⋮ Rational growth in virtually abelian groups ⋮ Geodesics with one self-intersection, and other stories ⋮ Growth in free groups (and other stories) -- twelve years later ⋮ Statistical limit laws for hyperbolic groups ⋮ Combinatorial growth in the modular group

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Mathematical Theory of Communication
• Growth in free groups (and other stories) -- twelve years later
• Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen
• Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen. II
• Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen. II. Nachtrag zu Math. Ann. 142, 385-398 (1961)
• Closed orbits in homology classes
• Closed geodesics in homology classes on surfaces of variable negative curvature
• Zeta functions of finite graphs and coverings. III
• On group-theoretic models of randomness and genericity.
• On the absence of McShane-type identities for the outer space
• Volume and bounded cohomology
• Geodesics in homology classes
• Asymptotics for closed geodesics in a homology class, the finite volume case
• Efficient computation of Fourier transforms on compact groups
• Zeta functions of finite graphs and coverings. II
• Perturbation theory for linear operators.
• Homology of closed geodesics in a negatively curved manifold
• Entropy and rigidity of locally symmetric spaces of strictly negative curvature
• Zeta functions of finite graphs and coverings
• Growth of the number of simple closed geodesics on hyperbolic surfaces
• Densities in free groups and \(\mathbb{Z}^k\), visible points and test elements.
• The Patterson-Sullivan embedding and minimal volume entropy for outer space.
• Number of cyclically irreducible words in the alphabet of a free group of finite rank
• Walks on groups, counting reducible matrices, polynomials, and surface and free group automorphisms
• On discrete subgroups of the two by two projective linear group over \(p\)-adic fields
• Applications of ergodic theory to the investigation of manifolds of negative curvature
• A simpler proof of Mirzakhani's simple curve asymptotics
• The Chebotarov theorem for Galois coverings of Axiom A flows
• Zariski Density and Genericity
• Combable functions, quasimorphisms, and the central limit theorem
• Discrete logarithms in free groups
• ASYMPTOTIC GROWTH OF CONJUGACY CLASSES IN FINITELY-GENERATED FREE GROUPS
• Minimal volume entropy for graphs
• Equidistribution of geodesics on homology classes and analogues for free groups
• Homology of Closed Geodesics in Certain Riemannian Manifolds
• Closed Geodesics on a Riemann Surface With Application to the Markov Spectrum
• Homology and Closed Geodesics in a Compact Riemann Surface
• Symmetrized Chebyshev polynomials
• THE IHARA-SELBERG ZETA FUNCTION OF A TREE LATTICE
• Symbolic Dynamics for Hyperbolic Flows
• Chebyshev's Bias
• Walks on graphs and lattices – effective bounds and applications
• Asymptotic winding of the geodesic flow on modular surfaces and continuous fractions
• Simple curves on surfaces
• Local limit theorems for free groups

This page was built for publication: Growth in free groups (and other stories) -- twelve years later