Tata Institute of Fundamental Research
Compactness and Large Deviations
STCS Colloquium
Speaker:
Chiranjib Mukherjee (Courant Institute of Mathematical Sciences
New York University
Warren Weaver Hall 1310
251 Mercer Street
New York, NY 10012
United States of America)
Organiser:
Sandeep K Juneja
Date:
Tuesday, 3 Oct 2017, 16:00 to 17:00
Venue:
A-201 (STCS Seminar Room)
(Scan to add to calendar)
Abstract:
In a reasonable topological space, large deviation estimates essentially deal with probabilities of events that are asymptotically (exponentially) small, and in a certain sense, quantify the rate of these decaying probabilities. In such estimates, upper bounds for such small probabilities often require compactness of the ambient space, which is often absent in problems arising in statistical mechanics (for example, distributions of local times of Brownian motion in the full space $\mathbb{R}^d$). Motivated by such a problem, we present a robust theory of ``translation-invariant compacti cation" of probability measures in $\mathbb{R}^d$. Thanks to an inherent shift-invariance of the underlying problem, we are able to apply this abstract theory painlessly and solve a long standing problem in statistical mechanics, the mean- eld polaron problem.
This talk is based on joint works with S.R.S. Varadhan (New York), as well as with Erwin Bolthausen (Zurich) and Wolfgang Koenig (Berlin).
| Speaker: | Chiranjib Mukherjee (Courant Institute of Mathematical Sciences New York University Warren Weaver Hall 1310 251 Mercer Street New York, NY 10012 United States of America) |
| Organiser: | Sandeep K Juneja |
| Date: | Tuesday, 3 Oct 2017, 16:00 to 17:00 |
| Venue: | A-201 (STCS Seminar Room) |
(Scan to add to calendar)
Abstract:
In a reasonable topological space, large deviation estimates essentially deal with probabilities of events that are asymptotically (exponentially) small, and in a certain sense, quantify the rate of these decaying probabilities. In such estimates, upper bounds for such small probabilities often require compactness of the ambient space, which is often absent in problems arising in statistical mechanics (for example, distributions of local times of Brownian motion in the full space $\mathbb{R}^d$). Motivated by such a problem, we present a robust theory of ``translation-invariant compacti cation" of probability measures in $\mathbb{R}^d$. Thanks to an inherent shift-invariance of the underlying problem, we are able to apply this abstract theory painlessly and solve a long standing problem in statistical mechanics, the mean- eld polaron problem.
This talk is based on joint works with S.R.S. Varadhan (New York), as well as with Erwin Bolthausen (Zurich) and Wolfgang Koenig (Berlin).
This talk is based on joint works with S.R.S. Varadhan (New York), as well as with Erwin Bolthausen (Zurich) and Wolfgang Koenig (Berlin).