\(R\)-positivity and the existence of zero-temperature limits of Gibbs measures on nearest-neighbor matrices

DOI10.1017/JPR.2023.59MaRDI QIDQ6500026

Jorge Littin Curinao, Gerardo Corredor Rincón

Publication date: 10 May 2024

Published in: Journal of Applied Probability (Search for Journal in Brave)

zbMATH Keywords

\(R\)-positivitybirth-death chainszero-temperature limits

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Other physical applications of random processes (60K40) Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) (60J20)

Cites Work

• Unnamed Item
• Unnamed Item
• Zero temperature limits of Gibbs equilibrium states for countable Markov shifts
• \(R\)-positivity of nearest neighbor matrices and applications to Gibbs states
• Weak KAM methods and ergodic optimal problems for countable Markov shifts
• Random walks
• Eigenvalues of tridiagonal pseudo-Toeplitz matrices
• Non-negative matrices and Markov chains.
• Ergodic properties of nonnegative matrices. I
• Zero temperature limits of Gibbs-equilibrium states for countable alphabet subshifts of finite type
• Zero-temperature limit of one-dimensional Gibbs states via renormalization: the case of locally constant potentials
• A variational characterization of one-dimensional countable state Gibbs random fields
• Gibbs measures at temperature zero
• Zero-temperature phase diagram for double-well type potentials in the summable variation class
• Equilibrium states and zero temperature limit on topologically transitive countable Markov shifts
• Applied Probability and Queues
• A LARGE DEVIATION PRINCIPLE FOR THE EQUILIBRIUM STATES OF HÖLDER POTENTIALS: THE ZERO TEMPERATURE CASE
• A dynamical proof for the convergence of Gibbs measures at temperature zero

This page was built for publication: \(R\)-positivity and the existence of zero-temperature limits of Gibbs measures on nearest-neighbor matrices