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Article Dans Une Revue Inventiones Mathematicae Année : 2022

Large genus asymptotic geometry of random square-tiled surfaces and of random multicurves

Résumé

Abstract The volume $\mathcal {B}_{\Sigma }^{\textrm {comb}}({\mathbb {G}})$ of the unit ball—with respect to the combinatorial length function $\ell _{{\mathbb {G}}}$—of the space of measured foliations on a stable bordered surface $\Sigma $ appears as the prefactor of the polynomial growth of the number of multicurves on $\Sigma $. We find the range of $s \in {\mathbb {R}}$ for which $(\mathcal {B}_{\Sigma }^{\textrm {comb}})^{s}$, as a function over the combinatorial moduli spaces, is integrable with respect to the Kontsevich measure. The results depend on the topology of $\Sigma $, in contrast with the situation for hyperbolic surfaces where [6] recently proved an optimal square integrability.

Dates et versions

hal-03862245 , version 1 (21-11-2022)

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Vincent Delecroix, Élise Goujard, Peter Zograf, Anton Zorich. Large genus asymptotic geometry of random square-tiled surfaces and of random multicurves. Inventiones Mathematicae, 2022, 230 (1), pp.123-224. ⟨10.1007/s00222-022-01123-y⟩. ⟨hal-03862245⟩
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