Universality in interface growth models

Universality in interface growth models

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Martin Hairer , University of Warwick
Fine Hall 322

Over the past few years, there has been growing evidence, at the heuristic, the mathematically rigorous, and even the experimental level, that models of one-dimensional interface growth exhibit a "universal" behaviour at large scales. More precisely, it is conjectured that there exists a self-similar space-time process called the "KPZ fixed point" which attracts a very large class of microscopic models under suitable rescaling. It has also emerged that a certain ill-posed nonlinear stochastic PDE, the KPZ equation, has a "weak universality" property in the sense that large classes of models with a tuneable parameter converge to its solutions at intermediate scalings in the limit where the tuneable parameter is small. I will review some of the existing mathematical results supporting these conjectures and give an idea of the mathematical techniques involved in their proofs.