University of Heidelberg, **Applied Analysis Seminar**

Dr. Codina Cotar (Department of Statistical Science, University College, London)

Equality of the Jellium and Uniform Electron Gas next-order asymptotic terms for Riesz potentials

*INF 205, SR1*

Equality of the Jellium and Uniform Electron Gas next-order asymptotic terms for Riesz potentials

We consider two sharp next-order asymptotics problems, namely the asymptotics for the minimum energy for optimal point con figurations and the asymptotics for the many-marginals Optimal Transport, in both cases with Coulomb and Riesz costs with inverse power-law long-range interactions. The first problem describes the ground state of a Coulomb or Riesz gas, while the second appears as a semi-classical limit of the Density Functional Theory energy modelling a quantum version of the same system. Recently the second-order term in these expansions was precisely described, and corresponds respectively to a Jellium and to a Uniform Electron Gas model. The present work shows that for inverse-power-law interactions with power d-2<s<d, the two problems have the same minimum.

This is based on joint works with Mircea Petrache.

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