Phases in large combinatorial systems

  • Charles Radin

    University of Texas, Austin, USA

Abstract

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.

Cite this article

Charles Radin, Phases in large combinatorial systems. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 5 (2018), no. 2, pp. 287–308

DOI 10.4171/AIHPD/55