Mini-course on Geometric Functional Inequalities for Markov Chains

Add to your list(s) Download to your calendar using vCal

• Sam Power (University of Bristol)
• Tuesday 03 December 2024, 14:00-16:00
• Seminar Room 2, Newton Institute.

If you have a question about this talk, please contact nobody.

SSD - Stochastic systems for anomalous diffusion

When analysing the long-time behaviour of Markov processes, many familiar techniques are quite probabilistic in nature, drawing on ‘pathwise’ perspectives like couplings, regenerations, and similar. A complementary approach is more functional-analytic in character, rather focusing directly on the { generator, semigroup, energy functionals, ... }  associated to the process. In some settings, these techniques can be quite appealing, being robustly applicable to a wide range of processes while often yielding quantitatively sharp bounds. The overall goal of this mini-course will be to provide a friendly introduction to the functional-analytic approach, to an intended audience who are perhaps more familiar with probabilistic techniques. Some more specific goals will be:

to introduce the ‘standard’ functional inequalities, to provide intuition for when they ‘ought to’ hold, and for their consequences, to clarify the practical settings to which the functional-analytic approach is well-suited, to highlight the simplicity and robustness of the functional-analytic approach in these cases, and to elucidate the compatibility of probabilistic techniques with the functional-analytic approach

The first part of the mini-course will review functional inequalities in the classical case of reversible diffusion processes, wherein many of the mathematical objects of interest are particularly interpretable. The second part of the mini-course will then cover how these inequalities apply in the setting of discrete-time Markov chains, which is expected to be of particular interest to attendees working on MCMC algorithms. Due to time constraints, I may not be able to provide detailed derivations for all results of interest. A secondary goal of the mini-course will then be to provide a suitably rich range of references which will enable the audience to fearlessly enter the literature on functional inequalities in their own time.

This talk is part of the Isaac Newton Institute Seminar Series series.

This talk is included in these lists:

• All CMS events
• Featured lists
• INI info aggregator
• Isaac Newton Institute Seminar Series
• School of Physical Sciences
• Seminar Room 2, Newton Institute
• bld31

Note that ex-directory lists are not shown.