Annales de l’Institut Henri Poincaré D


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Volume 5, Issue 2, 2018, pp. 287–308
DOI: 10.4171/AIHPD/55

Published online: 2018-06-04

Phases in large combinatorial systems

Charles Radin[1]

(1) University of Texas, Austin, USA

This is a status report on a companion subject to extremal combinatorics, obtained by replacing extremality properties with emergent structure, ‘phases’. We discuss phases, and phase transitions, in large graphs and large permutations, motivating and using the asymptotic formalisms of graphons for graphs and permutons for permutations. Phase structure is shown to emerge using entropy and large deviation techniques.

Keywords: Extremal combinatorics, emergent phases

Radin Charles: Phases in large combinatorial systems. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 5 (2018), 287-308. doi: 10.4171/AIHPD/55