The Razumov-Stroganov conjecture: Stochastic processes, loops and combinatorics

Abstract

A fascinating conjectural connection between statistical mechanics and combinatorics has in the past five years led to the publication of a number of papers in various areas, including stochastic processes, solvable lattice models and supersymmetry. This connection, known as the Razumov-Stroganov conjecture, expresses eigenstates of physical systems in terms of objects known from combinatorics, which is the mathematical theory of counting. This note intends to explain this connection in light of the recent papers by Zinn-Justin and Di Francesco.

6 pages, 4 figures, JSTAT News & Perspectives

References in corpus (8)

• Spin chains and combinatorics
• The quantum symmetric XXZ chain at Delta=-1/2, alternating sign matrices and plane partitions
• The Importance of being Odd
• Quantum Knizhnik-Zamolodchikov equation, generalized Razumov-Stroganov sum rules and extended Joseph polynomials
• The raise and peel model of a fluctuating interface
• Quantum Knizhnik-Zamolodchikov equation: reflecting boundary conditions and combinatorics
• Quantum incompressibility and Razumov Stroganov type conjectures
• Loop model with mixed boundary conditions, qKZ equation and alternating sign matrices

Cited by in corpus (3)

• On the weighted enumeration of alternating sign matrices and descending plane partitions
• Multiply-refined enumeration of alternating sign matrices
• Avalanches in the Raise and Peel model in the presence of a wall