Zobrazeno 1 - 10
of 1 708
pro vyhledávání: '"82B44"'
Autor:
Yau, Horng-Tzer, Yin, Jun
Consider an $ N \times N$ Hermitian one-dimensional random band matrix with band width $W > N^{1 / 2 + \varepsilon} $ for any $ \varepsilon > 0$. In the bulk of the spectrum and in the large $ N $ limit, we obtain the following results: (i) The semic
Externí odkaz:
http://arxiv.org/abs/2501.01718
Autor:
Chen, Hong-Bin
Recently, [arXiv:2311.08980] demonstrated that, if it exists, the limit free energy of possibly non-convex spin glass models must be determined by a characteristic of the associated infinite-dimensional non-convex Hamilton-Jacobi equation. In this wo
Externí odkaz:
http://arxiv.org/abs/2412.20610
Autor:
Chen, Hong-Bin
We consider the Potts spin glass with additional ferromagnetic interaction parametrized by $t$. It has long been observed that the Potts color symmetry breaking for the spin glass order parameter is closely related to the ferromagnetic phase transiti
Externí odkaz:
http://arxiv.org/abs/2412.20607
We consider the long-range random field Ising model in dimension $d = 1, 2$, whereas the long-range interaction is of the form $J_{xy} = |x-y|^{-\alpha}$ with $1< \alpha < 3/2$ for $d=1$ and with $2 < \alpha \leq 3$ for $d = 2$. Our main results esta
Externí odkaz:
http://arxiv.org/abs/2412.19281
Autor:
Ried, Tobias, Wagner, Christian
We consider a model of random curves in the plane related to the large-scale behavior of the Random Field Ising Model (RFIM) at temperature zero in two space dimensions. Our work is motivated by attempts to quantify the Imry--Ma phenomenon concerning
Externí odkaz:
http://arxiv.org/abs/2412.17625
Autor:
Cheairi, Houssam El, Gamarnik, David
Universality, namely distributional invariance, is a well-known property for many random structures. For example it is known to hold for a broad range of variational problems with random input. Much less is known about the universality of the perform
Externí odkaz:
http://arxiv.org/abs/2412.18014
Autor:
Dubova, Sofiia, Yang, Kevin
We study a class of Gaussian random band matrices of dimension $N \times N$ and band-width $W$. We show that delocalization holds for bulk eigenvectors and that quantum diffusion holds for the resolvent, all under the assumption that $W \gg N^{8/11}$
Externí odkaz:
http://arxiv.org/abs/2412.15207
In these lecture notes, we review recent progress in the study of the stochastic heat equation and its discrete analogue, the directed polymer model, in spatial dimension 2. It was discovered that a phase transition emerges on an intermediate disorde
Externí odkaz:
http://arxiv.org/abs/2412.10311
We consider mean-field vector spin glasses with possibly non-convex interactions. Up to a small perturbation of the parameters defining the model, the asymptotic behavior of the Gibbs measure is described in terms of a critical point of an explicit f
Externí odkaz:
http://arxiv.org/abs/2411.14105
Autor:
Chen, Hong-Bin
In [arXiv:2311.08980], it was shown that if the limit of the free energy in a non-convex vector spin glass model exists, it must be a critical value of a certain functional. In this work, we extend this result to multi-species spin glass models with
Externí odkaz:
http://arxiv.org/abs/2411.13342