相关论文: Bounds on the covariance matrix of the Sherrington…
In this paper, the fractional Hardy-type operator of variable order $\beta(x)$ is shown to be bounded from the variable exponent Herz-Morrey spaces $M\dot{K}_{p_{_{1}},q_{_{1}}(\cdot)}^{\alpha(\cdot),\lambda}(\R^{n})$ into the weighted…
Some recent results concerning the Sherrington-Kirkpatrick model are reported. For $T$ near the critical temperature $T_c$, the replica free energy of the Sherrington-Kirkpatrick model is taken as the starting point of an expansion in…
Consider an FPU chain composed of $N\gg 1$ particles, and endow the phase space with the Gibbs measure corresponding to a small temperature $\beta^{-1}$. Given a fixed $K<N$, we construct $K$ packets of normal modes whose energies are…
The ferromagnetic Ising model is a model of a magnetic material and a central topic in statistical physics. It also plays a starring role in the algorithmic study of approximate counting: approximating the partition function of the…
The rate of convergence of the Gibbs sampler for the generalized one-dimensional Ising model is determined by the second largest eigenvalue of its transition matrix in absolute value denoted by $\beta^*$. In this paper we generalize a…
We obtain (up to logarithmic scaling) the power-law lower bound $M_{p}(T_{k})\gtrsim T_{k}^{(1-\delta)p}$ on a subsequence $T_{k}\rightarrow\infty$, uniformly across $p>0$, for discrete one-dimensional quasiperiodic Schr\"odinger operators…
A generalization of the Sherrington-Kirkpatrick (SK) model for spin glasses is considered, in which the interaction matrix is endowed with a variance profile that has no particular structure an may be sparse. In the first part of this…
In this paper, the fractional Hardy-type operator of variable order $\beta(x)$ is shown to be bounded from the Herz-Morrey spaces $M\dot{K}_{p_{_{1}},q_{_{1}}(\cdot)}^{\alpha,\lambda}(\mathbb{R}^{n})$ with variable exponent $q_{1}(x)$ into…
From the study of a functional equation of Gibbs measures we calculate the limiting free energy of the Sherrington-Kirkpatrick spin glass model at a particular value of (low) temperature. This implies the following lower bound for the…
We obtain lower and upper bounds on the heat kernel and Green functions of the Schroedinger operator in a random Gaussian magnetic field and a fixed scalar potential. We apply stochastic Feynman-Kac representation, diamagnetic upper bounds…
The paper gives a bound on the generalization error of the Gibbs algorithm, which recovers known data-independent bounds for the high temperature range and extends to the low-temperature range, where generalization depends critically on the…
We prove a hardness of sampling result for the anti-ferromagnetic Ising model on random graphs of average degree $d$ for large constant $d$, proving that when the normalized inverse temperature satisfies $\beta>1$ (asymptotically…
We construct an extensive adiabatic invariant for a Klein-Gordon chain in the thermodynamic limit. In particular, given a fixed and sufficiently small value of the coupling constant $a$, the evolution of the adiabatic invariant is…
Let $n\ge 2$ and $s\in (n-2,n)$. Assume that $\Omega\subset \mathbb{R}^n$ is a one-sided bounded non-tangentially accessible domain with $s$-Ahlfors regular boundary and $\sigma$ is the surface measure on the boundary of $\Omega$, denoted…
We demonstrate that quantum mechanics entails a fundamental lower bound on the thermalization time $\tau$ of any system. At finite temperature, we show that $\tau$ is bounded by half the Planckian dissipation time, $\tau \geq \tau_{\rm…
A version of quantum Cram\'{e}r-Rao bound dictates that the covariance of any set of operators is bounded by a product of the derivatives of expectation values and the inverse of quantum metric. We elaborate that because quantum metric…
Cox proportional hazards model with measurement error is investigated. In Kukush et al. (2011) [Journal of Statistical Research 45, 77-94] and Chimisov and Kukush (2014) [Modern Stochastics: Theory and Applications 1, 13-32] asymptotic…
The $N_f$-flavour Schwinger Model on a finite space $0\leq x^1\leq L$ and subject to bag-type boundary-conditions at $x^1=0$ und $x^1=L$ is solved at finite temperature $T=1/\beta$. The boundary conditions depend on a real parameter…
Inspired by recent results in the context of AdS/CFT integrability, we reconsider the Thermodynamic Bethe Ansatz equations describing the 1D fermionic Hubbard model at finite temperature. We prove that the infinite set of TBA equations are…
We consider the macroscopic large N limit of the Circular beta-Ensemble at high temperature, and its weighted version as well, in the regime where the inverse temperature scales as beta/N for some parameter beta>0. More precisely, in the…