Related papers: Invariant measures for integrable spin chains and …
In this letter, I develop a new topologically invariant coherent state path integral for spin systems, and apply it to the quantum Heisenberg model on a square lattice. As a result, the quantum nonlinear $\sigma$ model for arbitrary values…
The BBM equation is a Hamiltonian PDE which revealed to be a very interesting test-model to study the transformation property of Gaussian measures along the flow. In this paper we study the BBM equation with critical dispersion (which is a…
We prove pathwise uniqueness for a class of stochastic differential equations (SDE) on a Hilbert space with cylindrical Wiener noise, whose nonlinear drift parts are sums of the sub-differential of a convex function and a bounded part. This…
This note, mostly expository, is devoted to Poincar{\'e} and log-Sobolev inequalities for a class of Boltzmann-Gibbs measures with singular interaction. Such measures allow to model one-dimensional particles with confinement and singular…
Lattice gauge theories are a powerful language to theoretically describe a variety of strongly correlated systems, including frustrated magnets, high-$T_c$ superconductors, and topological phases. However, in many cases gauge fields couple…
We propose and analyse a novel, fully discrete numerical algorithm for the approximation of the generalised Stokes system forced by transport noise -- a prototype model for non-Newtonian fluids including turbulence. Utilising the Gradient…
An exactly integrable symplectic correspondence is derived which in a continuum limit leads to the equations of motion of the relativistic generalization of the Calogero-Moser system, that was introduced for the first time by Ruijsenaars…
It is shown that white noise is an invariant measure for the Korteweg-deVries equation on $\mathbb T$. This is a consequence of recent results of Kappeler and Topalov establishing the well-posedness of the equation on appropriate negative…
We consider a sequence of finite irreducible Markov chains with exponentially small transition rates: the transition graph is a fixed, finite, strongly connected directed graph; the transition rates decay exponentially on a paramenter N…
We study invariant measures for random countable (finite or infinite) conformal iterated function systems (IFS) with arbitrary overlaps. We do not assume any type of separation condition. We prove, under a mild assumption of finite entropy,…
We initiate a systematic study of the convolution operation on Keisler measures, generalizing the work of Newelski in the case of types. Adapting results of Glicksberg, we show that the supports of generically stable (or just definable,…
In this paper, we build a Gibbs measure for the cubic defocusing Schr\"odinger equation on the real line with a decreasing interaction potential, in the sense that the non linearity $|u|^2u$ is multiplied by a function $\chi$ which we…
The lattice Wess-Zumino model written in terms of the Ginsparg-Wilson relation is invariant under a generalized supersymmetry transformation which is determined by an iterative procedure in the coupling constant. By studying the associated…
It was recently proposed in https://journals.aps.org/pre/abstract/10.1103/PhysRevE.94.043322 [Herdeiro & Doyon Phys.,Rev.,E (2016)] a numerical method showing a precise sampling of the infinite plane 2d critical Ising model for finite…
Disagreement percolation connects a Gibbs lattice gas and i.i.d. site percolation on the same lattice such that non-percolation implies uniqueness of the Gibbs measure. This work generalises disagreement percolation to the hard-sphere model…
This paper deals with the existence and limiting behavior of invariant measures of the stochastic Landau-Lifshitz-Bloch equation driven by linear multiplicative noise and additive noise defined in the entire space $\mathbb{R}^d$ for…
We investigate and prove the mathematical properties of a general class of one-dimensional unimodal smooth maps perturbed with a heteroscedastic noise. Specifically, we investigate the stability of the associated Markov chain, show the weak…
Approximating the invariant measure and the expectation of the functionals for parabolic stochastic partial differential equations (SPDEs) with non-globally Lipschitz coefficients is an active research area and is far from being well…
The discrete Frenet equation entails a local framing of a discrete, piecewise linear polygonal chain in terms of its bond and torsion angles. In particular, the tangent vector of a segment is akin the classical O(3) spin variable. Thus…
The classical Heisenberg model in two spatial dimensions constitutes one of the most paradigmatic spin models, taking an important role in statistical and condensed matter physics to understand magnetism. Still, despite its paradigmatic…