Temperley-Lieb Stochastic Processes

Abstract

We discuss one-dimensional stochastic processes defined through the Temperley-Lieb algebra related to the Q=1 Potts model. For various boundary conditions, we formulate a conjecture relating the probability distribution which describes the stationary state, to the enumeration of a symmetry class of alternating sign matrices, objects that have received much attention in combinatorics.

9 pages LaTeX, 11 Postscript figures, minor changes

References in corpus (6)

• Bits and Pieces in Logarithmic Conformal Field Theory
• Spin chains and combinatorics
• Exact spectra of conformal supersymmetric nonlinear sigma models in two dimensions
• The quantum symmetric XXZ chain at Delta=-1/2, alternating sign matrices and plane partitions
• Combinatorial nature of ground state vector of O(1) loop model
• Critical Q=1 Potts Model and Temperley-Lieb Stochastic Processes

Cited by in corpus (48)

• Logarithmic Minimal Models
• Entanglement and dynamics of diffusion-annihilation processes with Majorana defects
• Magic in the spectra of the XXZ quantum chain with boundaries at Delta=0 and Delta=-1/2
• Exact expressions for correlations in the ground state of the dense O(1) loop model
• Holographic applications of logarithmic conformal field theories
• Logarithmic torus amplitudes
• The raise and peel model of a fluctuating interface
• Fusion algebra of critical percolation
• Quantum Knizhnik-Zamolodchikov equation: reflecting boundary conditions and combinatorics
• The puzzle of bulk conformal field theories at central charge c=0
• The XXZ spin chain at $\Delta =-1/2$: Bethe roots, symmetric functions and determinants
• On polynomials interpolating between the stationary state of a O(n) model and a Q.H.E. ground state
• Nonequilibrium stationary states and equilibrium models with long range interactions
• Sum rules for the ground states of the O(1) loop model on a cylinder and the XXZ spin chain
• Exact Ground State and Finite Size Scaling in a Supersymmetric Lattice Model
• Polynomial solutions of qKZ equation and ground state of XXZ spin chain at Delta = -1/2
• Solvable Critical Dense Polymers on the Cylinder
• Inhomogeneous loop models with open boundaries
• Stochastic processes and conformal invariance
• Raise and Peel Models of fluctuating interfaces and combinatorics of Pascal's hexagon
• Ground-state properties of a supersymmetric fermion chain
• Notes on non-trivial and logarithmic CFTs with c=0
• Boundary qKZ equation and generalized Razumov-Stroganov sum rules for open IRF models
• Punctured plane partitions and the q-deformed Knizhnik--Zamolodchikov and Hirota equations
• When finite-size corrections vanish: The S=1/2 XXZ model and the Razumov-Stroganov state
• Exact finite size groundstate of the O(n=1) loop model with open boundaries
• Loop model with mixed boundary conditions, qKZ equation and alternating sign matrices
• Factorised solutions of Temperley-Lieb $q$KZ equations on a segment
• Open boundary Quantum Knizhnik-Zamolodchikov equation and the weighted enumeration of Plane Partitions with symmetries
• Finite-size corrections for universal boundary entropy in bond percolation
• Connectivity patterns in loop percolation I: the rationality phenomenon and constant term identities
• Proof of Razumov-Stroganov conjecture for some infinite families of link patterns
• The pair annihilation reaction D + D --> 0 in disordered media and conformal invariance
• Different facets of the raise and peel model
• Power-law entanglement and Hilbert space fragmentation in non-reciprocal quantum circuits
• Brauer loops and the commuting variety
• A_k Generalization of the O(1) Loop Model on a Cylinder: Affine Hecke Algebra, q-KZ Equation and the Sum Rule
• The dilute Temperley-Lieb O($n=1$) loop model on a semi infinite strip: the sum rule
• Refined Razumov-Stroganov conjectures for open boundaries
• The dilute Temperley-Lieb O($n=1$) loop model on a semi infinite strip: the ground state
• Critical site percolation on the triangular lattice: From integrability to conformal partition functions
• Fully packed loop models on finite geometries
• Currents in the dilute $O(n=1)$ model
• Finite size lattice results for the two-boundary Temperley--Lieb loop model
• Density profiles in the raise and peel model with and without a wall. Physics and combinatorics
• Cellular subalgebras of the partition algebra
• Critical behavior in a non-local interface model
• Avalanches in the Raise and Peel model in the presence of a wall