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Related papers: L\'evy Sachdev-Ye-Kitaev Model

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Traditional data-driven methods, effective for deterministic systems or stochastic differential equations (SDEs) with Gaussian noise, fail to handle the discontinuous sample paths and heavy-tailed fluctuations characteristic of L\'evy…

Dynamical Systems · Mathematics 2026-01-28 Yang Li , Jinqiao Duan

In a given market, financial covariances capture the intra-stock correlations and can be used to address statistically the bulk nature of the market as a complex system. We provide a statistical analysis of three SP500 covariances with…

Condensed Matter · Physics 2007-05-23 Z. Burda , J. Jurkiewicz , M. A. Nowak , G. Papp , I. Zahed

We consider a multivariate heavy-tailed stochastic volatility model and analyze the large-sample behavior of its sample covariance matrix. We study the limiting behavior of its entries in the infinite-variance case and derive results for…

Probability · Mathematics 2016-05-10 Anja Janßen , Thomas Mikosch , Mohsen Rezapour , Xiaolei Xie

The SYK model consists of $N\gg 1$ fermions in $0+1$ dimensions with a random, all-to-all quartic interaction. Recently, Kitaev has found that the SYK model is maximally chaotic and has proposed it as a model of holography. We solve the…

High Energy Physics - Theory · Physics 2016-05-04 Joseph Polchinski , Vladimir Rosenhaus

We point out that a classical analog of the Sachdev-Ye-Kitaev model -- a solvable model of quantum many-body chaos, was studied long ago in the turbulence literature. Motivated by the Navier-Stokes equation in the turbulent regime and the…

High Energy Physics - Theory · Physics 2024-01-17 Xu-Yao Hu , Vladimir Rosenhaus

The Sachdev-Ye-Kitaev (SYK) model is a concrete solvable model to study non-Fermi liquid properties, holographic duality and maximally chaotic behavior. In this work, we consider a generalization of the SYK model that contains two SYK…

Strongly Correlated Electrons · Physics 2017-11-22 Xin Chen , Ruihua Fan , Yiming Chen , Hui Zhai , Pengfei Zhang

We propose a simple solvable variant of the Sachdev-Ye-Kitaev (SYK) model which displays a quantum phase transition from a fast-scrambling non-Fermi liquid to disordered Fermi liquid. Like the canonical SYK model, our variant involves a…

Strongly Correlated Electrons · Physics 2019-07-24 Oguzhan Can , Marcel Franz

After a short excursion from discovery of Brownian motion to the Richardson "law of four thirds" in turbulent diffusion, the article introduces the L\'{e}vy flight superdiffusion as a self-similar L\'{e}vy process. The condition of…

Statistical Mechanics · Physics 2015-05-13 A. A. Dubkov , B. Spagnolo , V. V. Uchaikin

The L\'evy-stable distribution is the attractor of distributions which hold power laws with infinite variance. This distribution has been used in a variety of research areas, for example in economics it is used to model financial market…

Statistical Mechanics · Physics 2018-07-11 Karina Arias-Calluari , Fernando Alonso-Marroquin , Michael Harre

We analyze statistics for eigenvector entries of heavy-tailed random symmetric matrices (also called L\'{e}vy matrices) whose associated eigenvalues are sufficiently small. We show that the limiting law of any such entry is non-Gaussian,…

Probability · Mathematics 2020-11-13 Amol Aggarwal , Patrick Lopatto , Jake Marcinek

Recently, studies have explored the statistics of matrix elements of local operators in the Lieb-Liniger model. It was found that the probability distribution function for off-diagonal matrix elements $\langle…

Statistical Mechanics · Physics 2026-04-07 Tingfei Li , Shuanghong Li

We establish the integrability of a family of Sachdev-Ye-Kitaev (SYK) models with uniform $p$-body interactions. We derive the R-matrix and mutually commuting transfer matrices that generate the Hamiltonians of these models, and obtain…

Statistical Mechanics · Physics 2026-03-05 Kohei Fukai , Hosho Katsura

We study the electromagnetic transmission $T$ through one-dimensional (1D) photonic heterostructures whose random layer thicknesses follow a long-tailed distribution --L\'evy-type distribution. Based on recent predictions made for 1D…

The Sachdev-Ye-Kitaev (SYK) model describes Majorana fermions with random interaction, which displays many interesting properties such as non-Fermi liquid behavior, quantum chaos, emergent conformal symmetry and holographic duality. Here we…

High Energy Physics - Theory · Physics 2017-09-13 Yiming Chen , Hui Zhai , Pengfei Zhang

The Sachdev-Ye-Kitaev (SYK) model is of paramount importance for the understanding of both strange metals and a microscopic theory of two-dimensional gravity. We study the interplay between Stabilizer R\'enyi Entropy (SRE) and entanglement…

Quantum Physics · Physics 2025-12-09 Barbara Jasser , Jovan Odavić , Alioscia Hamma

We study a quantum mechanical model proposed by Sachdev, Ye and Kitaev. The model consists of $N$ Majorana fermions with random interactions of a few fermions at a time. It it tractable in the large $N$ limit, where the classical variable…

High Energy Physics - Theory · Physics 2016-11-09 Juan Maldacena , Douglas Stanford

We report on the emergence of scaling laws in the temporal evolution of the daily closing values of the S\&P 500 index prices and its modeling based on the L\'evy flights in two dimensions (2D). The efficacy of our proposed model is…

Statistical Finance · Quantitative Finance 2022-03-16 Hediye Yarahmadi , Abbas Ali Saberi

We construct examples of translationally invariant solvable models of strongly-correlated metals, composed of lattices of Sachdev-Ye-Kitaev dots with identical local interactions. These models display crossovers as a function of temperature…

Strongly Correlated Electrons · Physics 2018-07-27 Debanjan Chowdhury , Yochai Werman , Erez Berg , T. Senthil

The recent emergence of cryptocurrencies such as Bitcoin and Ethereum has posed possible alternatives to global payments as well as financial assets around the globe, making investors and financial regulators aware of the importance of…

Statistical Finance · Quantitative Finance 2021-07-02 Shinji Kakinaka , Ken Umeno

In this paper we consider an extension of the Rosenzweig-Porter (RP) model, the L\'evy-RP (L-RP) model, in which the off-diagonal matrix elements are broadly distributed, providing a more realistic benchmark to develop an effective…

Disordered Systems and Neural Networks · Physics 2021-03-31 Giulio Biroli , Marco Tarzia