Related papers: Invariant Gibbs dynamics for the dynamical sine-Go…
We study the learning dynamics of a multi-pass, mini-batch Stochastic Gradient Descent (SGD) procedure for empirical risk minimization in high-dimensional multi-index models with isotropic random data. In an asymptotic regime where the…
We construct the general permutation invariant Gaussian 2-matrix model for matrices of arbitrary size $D$. The parameters of the model are given in terms of variables defined using the representation theory of the symmetric group $S_D$. A…
The Randall-Sundrum model is studied in 6 dimension with AdS$_4$ or dS$_4$ metric in the physical 4 dimensional space. Two solutions are found, one with induced 5-dimensional gravity terms added to the induced cosmological constant terms.…
We examine the question of the integrability of the recently defined $\mathbb{Z}_2\times \mathbb{Z}_2$-graded sine-Gordon model, which is a natural generalisation of the supersymmetric sine-Gordon equation. We do this via appropriate…
Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the…
In this paper, we deal with random attractors for dynamical systems forced by a deterministic noise. These kind of systems are modeled as skew products where the dynamics of the forcing process are described by the base transformation.…
The sine-Gordon model is a paradigmatic quantum field theory that provides the low-energy effective description of many gapped 1D systems. Despite this fact, its complete thermodynamic description in all its regimes has been lacking. Here…
We consider stochastic dynamics of lattice systems with finite local state space, possibly at low temperature, and possibly non-reversible. We assume the additional regularity properties on the dynamics: a) There is at least one stationary…
The ground state of the $\SO(2n)_{1} \times \SO(2n)_{1} \over \SO(2n)_{2}$ coset theories, perturbed by the $\phi^{id,id}_{adj}$ operator and those of the sine-Gordon theory, for special values of the coupling constant in the attracting…
We investigate Sine$_\beta$, the universal point process arising as the thermodynamic limit of the microscopic scale behavior in the bulk of one-dimensional log-gases, or $\beta$-ensembles, at inverse temperature $\beta>0$. We adopt a…
We study non-perturbatively and from first principles the thermodynamics of vortices in 3d U(1) gauge+Higgs theory, or the Ginzburg-Landau model, which has frequently been used as a model for cosmological topological defect formation. We…
The G-Brownian-motion-driven stochastic differential equations (G-SDEs) as well as the G-expectation, which were seminally proposed by Peng and his colleagues, have been extensively applied to describing a particular kind of uncertainty…
In this paper we apply the exact solution of the sine-Gordon model to describe thermodynamic properties of the soliton liquid in the incommensurate phase of the double-layer quantum Hall systems. In this way we include thermal fluctuations…
We present solutions of asymmetric double sine-Gordon equation (DSGE) of an infinite system based on Mobius transformation and numerical exercise. This method is able to give the forms of the solutions for all the region on the \phi-\eta…
In the present paper we contribute to the thermodynamic formalism of partially hyperbolic attractors for local diffeomorphisms admitting an invariant stable bundle and a positively invariant cone field with non-uniform cone expansion at a…
We prove that at any inverse temperature $\beta$ and on any transitive amenable graph, the automorphism-invariant Gibbs states of the ferromagnetic Ising model are convex combinations of the plus and minus states. This is obtained for a…
We study the dissipative dynamics of one-dimensional fermions, described in terms of the sine-Gordon model in its free massive boson or semi-classical limit, while keeping track of forward scattering processes. The system is prepared in the…
We study a class of Gibbs measures of classical particle spin systems with spin space $S=\mathbb{R}^{m}$ and unbounded pair interaction, living on a metric graph given by a typical realization $\gamma $ of a random point process in…
We give a gauge invariant formulation of $N=2$ supersymmetric abelian Toda field equations in \n2 superspace. Superconformal invariance is studied. The conserved currents are shown to be associated with Drinfeld-Sokolov type gauges. The…
We develop a new robust technique to deduce variance principles for non-integrable discrete systems. To illustrate this technique, we show the existence of a variational principle for graph homomorphisms from $\Z^m$ to a $d$-regular tree.…