Alexander Holroyd

Bristol


Finitely Dependent Colouring


Combinatorics Seminar


1st November 2022, 11:00 am – 12:00 pm
Fry Building, 2.04


A central concept of probability and ergodic theory is mixing in its various forms. The strongest and simplest mixing condition is finite dependence, which states that variables at sufficiently well separated locations are independent. A 50-year old conundrum is to understand the relationship between finitely dependent processes and block factors (a block factor is a finite-range function of an independent family). The issue takes a surprising new turn if we in addition impose a local constraint (such as proper colouring) on the process. In particular, this has led to the discovery of a beautiful yet mysterious stochastic process that seemingly has no right to exist.






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