Spectral Gap Estimates in Mean Field Spin Glasses
Sign Up to like & getrecommendations! Published in 2017 at "Communications in Mathematical Physics"
DOI: 10.1007/s00220-018-3152-6
Abstract: We show that mixing for local, reversible dynamics of mean field spin glasses is exponentially slow in the low temperature regime. We introduce a notion of free energy barriers for the overlap, and prove that… read more here.
Keywords: spin glasses; mean field; spectral gap; field spin ... See more keywords
A Note on the Spectral Gap of the Fredrickson–Andersen One Spin Facilitated Model
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DOI: 10.1007/s10955-020-02666-1
Abstract: This note discusses the spectral gap of the Fredrickson–Andersen one spin facilitated model in two different settings. The model describes an interacting particle system on a graph, where each site is either occupied or empty;… read more here.
Keywords: gap; andersen one; spectral gap; one spin ... See more keywords
Spectral gap for measure-valued diffusion processes
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2019.123624
Abstract: The spectral gap is estimated for measure-valued diffusion processes induced by the intrinsic/extrinsic derivatives on the space of finite measures over a Riemannian manifold. This provides explicit exponential convergence rate for these processes to approximate… read more here.
Keywords: measure valued; spectral gap; valued diffusion; diffusion processes ... See more keywords
A nonvanishing spectral gap for AKLT models on generalized decorated graphs
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Mathematical Physics"
DOI: 10.1063/5.0139706
Abstract: We consider the spectral gap question for Affleck, Kennedy, Lieb, and Tasaki models defined on decorated versions of simple, connected graphs G. This class of decorated graphs, which are defined by replacing all edges of… read more here.
Keywords: nonvanishing spectral; spectral gap; physics; decorated graphs ... See more keywords
Aldous’s spectral gap conjecture for normal sets
Sign Up to like & getrecommendations! Published in 2020 at "Transactions of the American Mathematical Society"
DOI: 10.1090/tran/8155
Abstract: Let $G$ be a finite group and $\Sigma\subseteq G$ a symmetric subset. Every eigenvalue of the adjacency matrix of the Cayley graph $Cay\left(G,\Sigma\right)$ is naturally associated with some irreducible representation of $G$. Aldous' spectral gap… read more here.
Keywords: normal sets; gap conjecture; spectral gap; conjecture ... See more keywords
Finite plateau in spectral gap of polychromatic constrained random networks.
Sign Up to like & getrecommendations! Published in 2017 at "Physical Review E"
DOI: 10.1103/physreve.96.062309
Abstract: We consider critical behavior in the ensemble of polychromatic Erdős-Rényi networks and regular random graphs, where network vertices are painted in different colors. The links can be randomly removed and added to the network subject… read more here.
Keywords: gap polychromatic; finite plateau; plateau; polychromatic constrained ... See more keywords
Existence of a Spectral Gap in the Affleck-Kennedy-Lieb-Tasaki Model on the Hexagonal Lattice.
Sign Up to like & getrecommendations! Published in 2020 at "Physical review letters"
DOI: 10.1103/physrevlett.124.177204
Abstract: The S=1 Affleck-Kennedy-Lieb-Tasaki (AKLT) quantum spin chain was the first rigorous example of an isotropic spin system in the Haldane phase. The conjecture that the S=3/2 AKLT model on the hexagonal lattice is also in… read more here.
Keywords: gap; physics; lieb tasaki; spectral gap ... See more keywords
Spectral Gap-Based Seismic Survey Design
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Transactions on Geoscience and Remote Sensing"
DOI: 10.1109/tgrs.2023.3237464
Abstract: Seismic imaging in challenging sedimentary basins and reservoirs requires acquiring, processing, and imaging very large volumes of data (tens of terabytes). To reduce the cost of acquisition and the time from acquiring the data to… read more here.
Keywords: design; acquisition; survey design; spectral gap ... See more keywords
Estimating the spectral gap of a trace-class Markov operator
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DOI: 10.1214/19-ejs1563
Abstract: The utility of a Markov chain Monte Carlo algorithm is, in large part, determined by the size of the spectral gap of the corresponding Markov operator. However, calculating (and even approximating) the spectral gaps of… read more here.
Keywords: spectral gap; trace class; markov operator; markov ... See more keywords
Spectral gap and exponential mixing on geometrically finite hyperbolic manifolds
Sign Up to like & getrecommendations! Published in 2021 at "Duke Mathematical Journal"
DOI: 10.1215/00127094-2021-0051
Abstract: Let $\mathcal{M}=\Gamma\backslash\mathbb{H}^{d+1}$ be a geometrically finite hyperbolic manifold with critical exponent exceeding $d/2$. We obtain a precise asymptotic expansion of the matrix coefficients for the geodesic flow in $L^2(\mathrm{T}^1(\mathcal{M}))$, with exponential error term essentially as… read more here.
Keywords: geometrically finite; finite hyperbolic; exponential mixing; spectral gap ... See more keywords
Surgery of Graphs: M-Function and Spectral Gap
Sign Up to like & getrecommendations! Published in 2017 at "Acta Physica Polonica A"
DOI: 10.12693/aphyspola.132.1666
Abstract: We discuss behaviour of the spectral gap for quantum graphs when two metric graphs are glued together. It appears that precise answer to this question can be given using a natural generalisation of ... read more here.
Keywords: gap; function spectral; spectral gap; surgery graphs ... See more keywords