Local Behaviour of Airy Processes |
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Authors: | P R Pimentel Leandro |
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Institution: | 1.Instituto de Matemática, Universidade Federal do Rio de Janeiro, Av. Athos da Silveira Ramos 149, Centro de Tecnologia - Bloco C, Caixa Postal 68530, CEP 21941-909, Rio de Janeiro, RJ, Brazil ; |
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Abstract: | The Airy processes describe limit fluctuations in a wide range of growth models, where each particular Airy process depends on the geometry of the initial profile. We show how the coupling method, developed in the last-passage percolation context, can be used to prove existence of a continuous version and local convergence to Brownian motion. By using similar arguments, we further extend these results to a two parameter limit fluctuation process (Airy sheet). |
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