Phase diagram of the Potts model in an external magnetic field
Phase transition for the frog model.
Phase Transition in multicomponent systems.
Positive energy representations for quantum spin models in 1+1 dimensions
We present recent results on positive energy representations of quantum spin models.
Positivity of Lyapunov exponents for Anderson-type models on two coupled strings.
Prime percolation.
Probabilistic interpretation and random walk on spheres algorithms for the Poisson-Boltzmann equation in molecular dynamics
Motivated by the development of efficient Monte Carlo methods for PDE models in molecular dynamics, we establish a new probabilistic interpretation of a family of divergence form operators with discontinuous coefficients at the interface of two open subsets of . This family of operators includes the case of the linearized Poisson-Boltzmann equation used to compute the electrostatic free energy of a molecule. More precisely, we explicitly construct a Markov process whose infinitesimal generator...
Promotion operator on rigged configurations of type .
Proof of the Razumov-Stroganov conjecture for some infinite families of link patterns.
Propriétés ergodiques, en mesure infinie, de certains systèmes dynamiques fibrés
Quantum curve in -oscillator model.
Quantum detailed balance
Quantum detailed balance conditions with time reversal: the finite-dimensional case
We classify generators of quantum Markov semigroups on (h), with h finite-dimensional and with a faithful normal invariant state ρ satisfying the standard quantum detailed balance condition with an anti-unitary time reversal θ commuting with ρ, namely for all x,y ∈ and t ≥ 0. Our results also show that it is possible to find a standard form for the operators in the Lindblad representation of the generators extending the standard form of generators of quantum Markov semigroups satisfying the usual...
Quantum integrable 1D anyonic models: construction through braided Yang-Baxter equation.
Quantum integrable model of an arrangement of hyperplanes.
Quantum interfaces
We review recent results on interface states in quantum statistical mechanics.
Quantum relativistic Toda chain.
Quantum relativistic Toda chain at root of unity: isospectrality, modified -operator, and functional Bethe ansatz.
Quasi-periodic solutions of nonlinear random Schrödinger equations
Quasi-polynomial mixing of the 2D stochastic Ising model with “plus” boundary up to criticality
We considerably improve upon the recent result of [37] on the mixing time of Glauber dynamics for the 2D Ising model in a box of side at low temperature and with random boundary conditions whose distribution stochastically dominates the extremal plus phase. An important special case is when is concentrated on the homogeneous all-plus configuration, where the mixing time is conjectured to be polynomial in . In [37] it was shown that for a large enough inverse-temperature and any there...