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Central limit theorem for superdiffusive processes

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SSD - Stochastic systems for anomalous diffusion

We will present a few examples of superdiffusive processes, the main order asymptotic of which is characterised by a parameter beta of the model. As we will explain, these models all admit a similar phase transition: they satisfy a central limit theorem up to a critical value of the parameter beta, after which the CLT breaks apart as non-Gaussian corrections become prevalent. The case we will focus most attention on is that of an obliquely reflected Brownian motion in a generalised parabolic domain, for which we prove both the central limit theorem and its failure below the critical parameter. Based on a joint work with Aleksandar Mijatovic and Andrew Wade. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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