Alexander Povolotsky: Limit shapes and universal fluctuations

Recently the phenomena of appearance of limit shapes in various stochastic systems with many degrees of freedom attracted a lot of attention. Furthermore, the random fluctuations around these nonrandom limit shapes reveal universal behavior being described in terms of a few universal distributions and random processes. The examples are numerous, from random matrices and random tilings and traffic flows and polymers in random medium. We will give a brief review of the state of the field and consider simple exactly solvable examples.

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