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Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
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When is a stationary measure of a Markov chain "exponentially localized"?
I will give some answers in terms of diffusion processes, since the examples are easiest for me to describe in that context. There are more general examples which follow the same pattern, but typicall …