Ergodicity and Lyapunov functions for Langevin dynamics with singular potentials

dc.contributor.author

Herzog, DP

dc.contributor.author

Mattingly, JC

dc.date.accessioned

2017-11-30T20:52:28Z

dc.date.available

2017-11-30T20:52:28Z

dc.date.issued

2017-11-30

dc.description.abstract

We study Langevin dynamics of $N$ particles on $R^d$ interacting through a singular repulsive potential, e.g.~the well-known Lennard-Jones type, and show that the system converges to the unique invariant Gibbs measure exponentially fast in a weighted total variation distance. The proof of the main result relies on an explicit construction of a Lyapunov function. In contrast to previous results for such systems, our result implies geometric convergence to equilibrium starting from an essentially optimal family of initial distributions.

dc.identifier

http://arxiv.org/abs/1711.02250v1

dc.identifier.uri

https://hdl.handle.net/10161/15776

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Wiley

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math.PR

dc.subject

math.PR

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math-ph

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math.DS

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math.MP

dc.subject

60H10, 82C31, 37A25, 37B25

dc.title

Ergodicity and Lyapunov functions for Langevin dynamics with singular potentials

dc.type

Journal article

duke.contributor.orcid

Mattingly, JC|0000-0002-1819-729X

pubs.author-url

http://arxiv.org/abs/1711.02250v1

pubs.organisational-group

Duke

pubs.organisational-group

Mathematics

pubs.organisational-group

Statistical Science

pubs.organisational-group

Temp group - logins allowed

pubs.organisational-group

Trinity College of Arts & Sciences

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