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# Min Kang : Tropically Linear Interface Growth Models

We first discuss a general method to derive macroscopic laws from certain microscopic interactions that can be applied to a large class of particle systems. In particular we consider a broad class of systems that are linear in a special algebra, so-called tropical algebra. Some natural connections among the scaling limits of these random systems, the solutions to specific partial differential equations (Hamilton-Jacobi type) and combinatorial optimization problems have been noticed. If time allows, we further discuss a useful application of the variational formula (microscopic version of Hopf-Lax formula) to a well-known interacting particle system, totally asymmetric simple exclusion process.

**Category**: Applied Math and Analysis**Duration**: 01:34:47**Date**: November 27, 2006 at 4:25 PM-
**Tags:**seminar, Applied Math And Analysis Seminar

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