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The entropy of an ergodic source is the limit of properly rescaled 1-block entropies of sources obtained applying successive non-sequential recursive pairs substitutions (see P. Grassberger 2002 ArXiv:physics/0207023 and D. Benedetto, E. Caglioti and
Externí odkaz:
http://arxiv.org/abs/1007.3384
Publikováno v:
Letters in Mathematical Physics. 113
The universal typical-signal estimators of entropy and cross-entropy based on the asymptotics of recurrence and waiting times play an important role in information theory. Building on their construction, we introduce and study universal typical-signa
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1bedf6bd3f021b8706e9667abbf5de8a
https://doi.org/10.1007/s11005-023-01640-8
https://doi.org/10.1007/s11005-023-01640-8
We perform a statistical analysis of deterministic energy-decreasing algorithms on mean-field spin models with complex energy landscape like the Sine model and the Sherrington Kirkpatrick model. We specifically address the following question: in the
Externí odkaz:
http://arxiv.org/abs/cond-mat/0210545
The Random Orthogonal Model (ROM) of Marinari-Parisi-Ritort [MPR1,MPR2] is a model of statistical mechanics where the couplings among the spins are defined by a matrix chosen randomly within the orthogonal ensemble. It reproduces the most relevant pr
Externí odkaz:
http://arxiv.org/abs/cond-mat/0207681
Let $\{E_{\s}(N)\}_{\s\in\Sigma_N}$ be a family of $|\Sigma_N|=2^N$ centered unit Gaussian random variables defined by the covariance matrix $C_N$ of elements $\displaystyle c_N(\s,\tau):=\av{E_{\s}(N)E_{\tau}(N)}$, and $H_N(\s) = - \sqrt{N} E_{\s}(N
Externí odkaz:
http://arxiv.org/abs/math-ph/0206007
We consider the zero-temperature dynamics for the infinite-range, non translation invariant one-dimensional spin model introduced by Marinari, Parisi and Ritort to generate glassy behaviour out of a deterministic interaction. It is shown that there c
Externí odkaz:
http://arxiv.org/abs/cond-mat/0006476
We consider the infinite-range deterministic spin models with Hamiltonian $H=\sum_{i,j=1}^N J_{i,j}\sigma_i\sigma_j$, where $J$ is the quantization of a chaotic map of the torus. The mean field (TAP) equations are derived by summing the high temperat
Externí odkaz:
http://arxiv.org/abs/cond-mat/9605149
Publikováno v:
Commun.Math.Phys. 176 (1996) 73-94
We present a unified framework for the quantization of a family of discrete dynamical systems of varying degrees of "chaoticity". The systems to be quantized are piecewise affine maps on the two-torus, viewed as phase space, and include the automorph
Externí odkaz:
http://arxiv.org/abs/hep-th/9502035
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