Towards a Painlevé formula for PNG model with external sources in half-space

Occelli Alessandra, Université d'Angers

In this talk I will introduce a preliminary result concerning the distribution of a PNG model in half-space with two external sources. First I will present the strategy developed to study the model in the full space setting (Baik–Rains ’00); strategy which relies on algebraic and orthogonal polynomials identities, and Riemann–Hilbert techniques, and which led to a limit distribution formulated in terms of the solution to Painlevé II Riemann–Hilbert problem. I will try to underline the differences and the difficulties we face when looking at the asymptotic regime in half-space. Based on joint work with M. Cafasso, D. Ofner, H. Walsh.

Area: IS22 - Universality, Stochastic PDEs and Random Growth (Giuseppe Cannizzaro)

Keywords: PNG model

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