The Asymptotic Statistics of Random Covering Surfaces

DOI10.1017/fmp.2023.13zbMath1521.20016arXiv2003.05892OpenAlexW3011708210MaRDI QIDQ6161098

Doron Puder, Michael Magee

Publication date: 2 June 2023

Published in: Forum of Mathematics, Pi (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.05892

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Geometric group theory (20F65) Topological methods in group theory (57M07) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34) Symmetric groups (20B30) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15) Probabilistic methods in group theory (20P05) Algebraic geometry over groups; equations over groups (20F70) 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) (57K20)

Related Items (3)

Near optimal spectral gaps for hyperbolic surfaces ⋮ Determinants of Laplacians on random hyperbolic surfaces ⋮ Statistics of finite degree covers of torus knot complements

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Lectures on representations of surface groups
• On the growth of Betti numbers of locally symmetric spaces
• A new approach to representation theory of symmetric groups
• On generalised free products
• Poisson-Dirichlet distribution for random Belyi surfaces
• Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces
• Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
• Topology of finite graphs
• The symplectic nature of fundamental groups of surfaces
• On quantum gauge theories in two dimensions
• Recurrence of distributional limits of finite planar graphs
• Fuchsian groups, coverings of Riemann surfaces, subgroup growth, random quotients and random walks.
• Surface words are determined by word measures on groups
• Random unitary representations of surface groups. I: Asymptotic expansions
• Core surfaces
• Word measures on symmetric groups
• Quantifying residual finiteness.
• Matrix group integrals, surfaces, and mapping class groups. I. \(\mathrm{U}(\mathrm{n})\)
• On the growth of \(L^2\)-invariants for sequences of lattices in Lie groups
• A random cover of a compact hyperbolic surface has relative spectral gap \(\frac{3}{16}-\varepsilon\)
• Free Random Variables
• Subgroups of Surface Groups are Almost Geometric
• On the number of cycles of given length of a free word in several random permutations
• Character Theory of Symmetric Groups and Subgroup Growth of Surface Groups
• The Yang-Mills equations over Riemann surfaces
• A tour through Mirzakhani’s work on moduli spaces of Riemann surfaces
• Measure preserving words are primitive
• Residual Finiteness of Surface Groups
• The Hook Graphs of the Symmetric Group
• Geometry and spectra of compact Riemann surfaces
• The probability of generating the symmetric group

This page was built for publication: The Asymptotic Statistics of Random Covering Surfaces