相关论文: Bounds on the covariance matrix of the Sherrington…

We prove that the two point correlation matrix $ \textbf{M}= (\langle \sigma_i ; \sigma_j\rangle)_{1\leq i,j\leq N} \in \mathbb{R}^{N\times N}$ of the Sherrington-Kirkpatrick model has the property that for every $\epsilon>0$ there exists…

For an $N \times T$ random matrix $X(\beta)$ with weakly dependent uniformly sub-Gaussian entries $x_{it}(\beta)$ that may depend on a possibly infinite-dimensional parameter $\beta\in \mathbf{B}$, we obtain a uniform bound on its operator…

We consider the Sherrington--Kirkpatrick spin glass model with zero external field and at inverse temperature $\beta>0$. Let $F_N(\beta)$ be the corresponding log-partition function. Under the assumption that $c_N:=N^{1/3}(1-\beta_N^2)$ is…

We show that the two point correlation matrix $ \textbf{M}= (\langle \sigma_i \sigma_j\rangle)_{1\leq i,j\leq N} $ of the Sherrington-Kirkpatrick model with zero external field satisfies \[ \lim_{N\to\infty} \| \textbf{M} - ( 1+\beta^2 -…

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 extend two rigorous results of Aizenman, Lebowitz, and Ruelle in their pioneering paper of 1987 on the Sherrington-Kirkpatrick spin-glass model without external magnetic field to the quantum case with a "transverse field" of strength…

We show that in the Sherrington-Kirkpatrick model at inverse temperature $\beta$ with uniform external field $h>0$, replica symmetry holds in the regime $ \beta^2\mathrm{E}[ \mathrm{sech}^4(\beta\sqrt{q}Z+h)] \le 1$, where $Z$ is a standard…

We prove the existence of a critical regime for the fluctuations of the ground-state energy of the spherical Sherrington-Kirkpatrick model in an external field, confirming predictions given in [3,12]. We also establish a critical regime for…

We give a polynomial-time algorithm to sample from the Gibbs measure of the Sherrington-Kirkpatrick model with negligible total-variation distance (TVD) error up to inverse temperature $\beta < 1/2$. Prior work obtained TVD error guarantees…

In this paper, Hardy type operator $H_{\beta}$ on $\bR^{n}$ and its adjoint operator $H_{\beta}^{*}$ are investigated. We use novel methods to obtain two main results. One is that we obtain the operators $H_{\beta}$ and $H_{\beta}^{*}$…

Based on some new robust estimators of the covariance matrix, we propose stable versions of Principal Component Analysis (PCA) and we qualify it independently of the dimension of the ambient space. We first provide a robust estimator of the…

For open quantum systems coupled to a thermal bath at inverse temperature $\beta$, it is well known that under the Born-, Markov-, and secular approximations the system density matrix will approach the thermal Gibbs state with the bath…

Let $A$ be a finite set and $\phi:A^Z\to R$ be a locally constant potential. For each $\beta>0$ ("inverse temperature"), there is a unique Gibbs measure $\mu_{\beta\phi}$. We prove that, as $\beta\to+\infty$, the family…

We upper- and lower-bound the optimal precision with which one can estimate an unknown Hamiltonian parameter via measurements of Gibbs thermal states with a known temperature. The bounds depend on the uncertainty in the Hamiltonian term…

(R-channel) TBA is elaborated to find the effective central charge dependence on the boundary parameters for the massless boundary sine-Gordon model with the coupling constant $(8\pi) /\beta^2 = 1+ \lambda $ with $\lambda$ a positive…

We develop a cavity method in the spherical Sherrington-Kirkpatrick model at high temperature and small external field. As one application we compute the limit of the covariance matrix for fluctuations of the overlap and magnetization.

In this article we continue our investigations of one particle quantum scattering theory for Schroedinger operators on a set of connected (idealized one-dimensional) wires forming a graph with an arbitrary number of open ends. The…

In the present paper we obtain rates of convergence for the limit theorems of the density vector in the Curie-Weiss-Potts model via Stein's Method of exchangeable pairs. Our results include Kolmogorov bounds for multivariate normal…

We consider the Curie-Weiss Potts model in zero external field under independent symmetric spin-flip dynamics. We investigate dynamical Gibbs-non-Gibbs transitions for a range of initial inverse temperatures beta<3, which covers the phase…

We present two rigorous results on the Sherrington-Kirkpatrick mean field model for spin glasses, proven by elementary methods, based on properties of fluctuations, with respect to the external quenched noise, of the thermodynamic variables…