Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus
By Maryam Mirzakhani. 2010
161 citations recorded by the source corpus.
In this paper we study the asymptotic behavior of Weil-Petersson volumes of moduli spaces of hyperbolic surfaces of genus $g$ as $g \rightarrow \infty.$ We apply these asymptotic estimates to study the geometric properties of random hyperbolic surfaces, such as the Cheeger constant and the length of the shortest simple closed geodesic of a given combinatorial type.
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/65848f8524b3960c1469abf9c3d90ffda2633798
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In Geometry and Topology
Citations in the corpus
- Lengths of closed geodesics on random surfaces of large genus (2017, methodology): “nd we refer the reader to [MZ15] and the references therein for these. We will state only those bounds that we need. The bound on intersection numbers we will need, which can be found as Lemma 3.5 in [Mir13a], is the following: Lemma2.4. [Mir13a] Given n∈ N, there exists a constant c0 >0 independ”
- JT gravity and the ensembles of random matrix theory (2019, background): “Zograf’s formulas were motivated by comparison to explicit low-genus computations, but aspects of his conjectures were later established rigorously [110, 111].”
- JT gravity as a matrix integral (2019, background): “11Parts of this conjecture have been established rigorously [31, 70, 45].”
- Towards large genus asymptotics of intersection numbers on moduli spaces of curves (2011, background): “ 2 + k 2 +1/4 = 16(k−1+1/4), (3.11) lim g→∞ Be 1,g,n Vg−1,n+1 = 16 X∞ i=0 (i+1)(ai+1 −ai) = 4, and we also have Be k,g,n ≤ 16kVg−1,n+1. (3.12) 3. Contribution from (2.4). By the results obtained in [M3] X I∐J={2,...,n} 0≤g′≤g Vg′,|I|+1· Vg−g′,|J|+1 Vg,n = O 1 g2 . Put Sk1,k2,g,n = X I∐J={2,...,n}”