# On the large genus asymptotics of psi-class intersection numbers

@inproceedings{Guo2021OnTL, title={On the large genus asymptotics of psi-class intersection numbers}, author={Jindong Guo and Di Yang}, year={2021} }

Based on an explicit formula of the generating series for the n-point psi-class intersection numbers (cf. Bertola et. al. [4]), we give a novel proof of a conjecture of Delecroix et. al. [9] regarding the large genus uniform leading asymptotics of the psi-class intersection numbers. We also investigate polynomiality phenomenon in the large genera.

## References

SHOWING 1-10 OF 35 REFERENCES

Large genus asymptotics for intersection numbers and principal strata volumes of quadratic differentials

- MathematicsInventiones mathematicae
- 2021

In this paper we analyze the large genus asymptotics for intersection numbers between $\psi$-classes, also called correlators, on the moduli space of stable curves. Our proofs proceed through a…

Buryak–Okounkov Formula for the n-Point Function and a New Proof of the Witten Conjecture

- Mathematics, PhysicsInternational Mathematics Research Notices
- 2020

We identify the formulas of Buryak and Okounkov for the $n$-point functions of the intersection numbers of psi-classes on the moduli spaces of curves. This allows us to combine the earlier known…

An algebro-geometric proof of Witten's conjecture

- Mathematics
- 2007

We present a new proof of Witten's conjecture. The proof is based on the analysis of the relationship between intersection indices on moduli spaces of complex curves and Hurwitz numbers enumerating…

Weil-Petersson volumes and intersection theory on the moduli space of curves

- Mathematics
- 2006

In this paper, we establish a relationship between the Weil-Petersson volume Vgin(b) of the moduli space Mg,n(b) of hyperbolic Riemann surfaces with geodesic boundary components of lengths b\,...,bn,…

Correlation functions of the KdV hierarchy and applications to intersection numbers over M¯g,n

- Physics, Mathematics
- 2016

We derive an explicit generating function of correlations functions of an arbitrary tau-function of the KdV hierarchy. In particular applications, our formulation gives closed formulae of a new type…

Double ramification cycles and the $n$-point function for the moduli space of curves

- Mathematics, Physics
- 2016

In this paper, using the formula for the integrals of the $\psi$-classes over the double ramification cycles found by S. Shadrin, L. Spitz, D. Zvonkine and the author, we derive a new explicit…

A remark on Mirzakhani's asymptotic formulae

- Mathematics
- 2011

In this note, we answer a question of Mirzakhani on asymptotic behavior of the one-point volume polynomial of moduli spaces of curves. We also present some applications of Mirzakhani's asymptotic…

On Gromov – Witten invariants of P 1

- 2019

Here, (Σg, p1, . . . , pn) denotes an algebraic curve of genus g with at most double-point singularities as well as with the distinct marked points p1, . . . , pn, and the equivalence relation ∼ is…

Gromov-Witten theory, Hurwitz numbers, and Matrix models, I

- Mathematics, Physics
- 2001

The main goal of the paper is to present a new approach via Hurwitz numbers to Kontsevich's combinatorial/matrix model for the intersection theory of the moduli space of curves. A secondary goal is…

Geometry and arithmetic of integrable hierarchies of KdV type. I. Integrality

- Mathematics, Physics
- 2021

For each of the simple Lie algebras g = Al, Dl or E6, we show that the all-genera one-point FJRW invariants of g-type, after multiplication by suitable products of Pochhammer symbols, are the…