LTCC Intensive Course. Large Deviation Theory for Markov Processes: Spectral Theory, Variational Principles, and Beyond.

28 October 2024

COURSE SUMMARY:

Large deviation theory provides a mathematical framework for quantifying rare events in stochastic systems. This intensive course introduces the theory for continuous-time Markov processes, focusing on empirical observables such as occupation measures, currents, and time-integrated quantities. Topics include tilted generators and spectral methods, large deviations of empirical measures and flows (level-2.5 theory), variational formulations based on relative entropy, and connections with stochastic optimal control. The emphasis will be on developing intuition and methods through Markov process theory, spectral, and variational formulations, rather than a measure-theoretic treatment of large deviations. Depending on participants' interests, the course may also briefly cover numerical methods for rare event-sampling. The course will conclude with an outlook on current research directions, including recent developments and open problems in non-Markovian and self-interacting stochastic processes.

 

PREREQUISITES:

Participants should be familiar with probability theory, continuous-time Markov chains, stochastic differential equations, and basic linear algebra, including eigenvalue problems. Familiarity with generators of Markov processes or statistical mechanics will be helpful but is not required.

 

Start: Thursday 11th November 2026 from 1pm to 5pm
Finish: Friday 12th November 2026 from 9am to 1pm

 

Venue: UCL, Department of Mathmatics, Room 706, 7th Floor, 25 Gordon Street, London, WC1H 0AY.

 

Participants are asked to register by here: 

LTCC Intensive Course Registration Form 2026-2027 – Fill out form

or by emailing: office@ltcc.ac.uk