SMS scnews item created by Catherine Meister at Fri 24 Apr 2026 1633
Type: Seminar
Distribution: World
Expiry: 8 May 2026
Calendar1: 30 Apr 2026 1300-1400
CalLoc1: SMRI Seminar Room (A12 Macleay Room 301)
CalTitle1: Physical measures, intermittent dynamics and random walks
Auth: cmeister@159-196-153-133.9fc499.syd.nbn.aussiebb.net (cmei0631) in SMS-SAML

SMRI Seminar: Melbourne

Physical measures, intermittent dynamics and random walks

Ian Melbourne, University of Warwick

SMRI Seminar, Thursday 30th April 2026, 1 pm – 2 pm, SMRI Seminar Room (A12 Macleay Room 301)

Abstract: The classical Birkhoff ergodic theorem discusses almost sure convergence of time averages to space averages. (It is a generalisation of the strong law of large numbers in probability theory.) However, in examples the almost sure convergence is often on a set of zero volume in phase space. A physical measure is one where convergence of time averages to space averages holds for continuous observables on a set of positive volume. Equivalently, a physical measure is one that is the weak* limit of empirical measures on a set of positive volume. We consider systems with no physical measure and characterise the weak* limits and distributional limits of empirical measures in such situations. Examples include intermittent maps, random walks on the integers and random walks on Y-shaped regions (imagine the integers with 3 (several) directions and 3 (several) points at infinity). As far as we know, our results are new even for the simple symmetric random walk on the integers.
This is joint work with Douglas Coates and Amin Talebi.

For seminar updates, see our What's On Calendar. Please join us after the seminar for the SMRI afternoon tea, every Thursday at 2 pm on the SMRI Terrace.

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