Related papers: A unified stability property in spin glasses
In this article, let $\Sigma\subset\R^{2n}$ be a compact convex hypersurface which is $(r, R)$-pinched with $\frac{R}{r}<\sqrt{{3/2}}$. Then $\Sg$ carries at least two strictly elliptic closed characteristics; moreover, $\Sg$ carries at…
Explanation methods for machine learning models tend not to provide any formal guarantees and may not reflect the underlying decision-making process. In this work, we analyze stability as a property for reliable feature attribution methods.…
We consider the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential equations). We develop a general approach, based on…
We establish the uniform in time stability, w.r.t. the marginals, of the Iterative Proportional Fitting Procedure, also known as Sinkhorn algorithm, used to solve entropy-regularised Optimal Transport problems. Our result is quantitative…
We use real replicas within the Thouless, Anderson and Palmer construction to investigate stability of solutions with respect to uniform scalings in the phase space of the Sherrington-Kirkpatrick model. We show that the demand of…
The nature of the spin glass state is investigated by studying changes to the ground state when a weak perturbation is applied to the bulk of the system. We consider short range models in three and four dimensions and the infinite range…
Some invariances under perturbations of the spin glass phase are introduced, their proofs outlined and their consequences illustrated as factorisation rules for the overlap distribution. A comparison between the state of the art for mean…
While macroscopic properties of spin glasses have been thoroughly investigated, their manifestation in the corresponding microscopic configurations is much less understood. Cases where both descriptions have been provided, such as…
A simple model of a frustrated disordered system is presented. Apart from the (very different) physical interpretation, the model shares many features with that of Sherrington-Kirkpatrick for spin glasses, but, as a consequence of its…
We establish a strict asymptotic inequality between a class of graph partition problems on the sparse End\H{o]s-R\'enyi and random regular graph ensembles with the same average degree. Along the way, we establish a variational…
The static and dynamic susceptibilities for a general class of mean field random orthogonal spherical spin glass models are studied. We show how the static and dynamical properties of the linear and nonlinear susceptibilities depend on the…
Suppose that two vector fields on a smooth manifold render some equilibrium point globally asymptotically stable (GAS). We show that there exists a homotopy between the corresponding semiflows such that this point remains GAS along this…
We present a theory to describe the dynamics of the Sherrington- Kirkpatrick spin-glass with (sequential) Glauber dynamics in terms of deterministic flow equations for macroscopic parameters. Two transparent assumptions allow us to close…
We study the linear stability of Einstein metrics of Riemannian submersion type. First, we derive a general instability condition for such Einstein metrics and provide some applications. Then we study instability arising from Riemannian…
On \'{e}tudie la covariance (pour la mesure de Gibbs) des spins en deux sites dans le cas d'un mod\`{e}le de Sherrington--Kirkpatrick avec champ externe; lorsque le nombre de sites du mod\`{e}le tend vers l'infini, une \'{e}valuation…
We develop a theory of generically stable and smooth Keisler measures in NIP metric theories, generalizing the case of classical logic. Using smooth extensions, we verify that fundamental properties of (Borel)-definable measures and the…
We consider short-range Ising spin glasses in equilibrium at infinite system size, and prove that, for fixed bond realization and a given Gibbs state drawn from a suitable metastate, each translation- and locally-invariant function (for…
We study numerically the out of equilibrium dynamics of the hypercubic cell spin glass in high dimensionalities. We obtain evidence of aging effects qualitatively similar both to experiments and to simulations of low dimensional models.…
We investigate the relevance of the conformal method by investigating stability issues for the Einstein-Lichnerowicz conformal constraint system in a nonlinear scalar-field setting. We prove the stability of the system with respect to…
We establish homological stability for automorphisms of symmetric bilinear forms over a class of principal ideal domains that includes all fields, the integers, the Gaussian integers, and the Eisenstein integers. In conjunction with…