2024 Gaussian multiplicative chaos

Gaussian multiplicative chaos

Author: qbli

August undefined, 2024

WebIn this article, we extend the theory of multiplicative chaos for positive definite functions in ℝd of the form f(x)=λ2ln+ R/ x +g(x), where g is a continuous and bounded function. The construction is simpler and more general than the one defined by Kahane in [Ann. Sci. Math. Québec 9 (1985) 105–150]. As a main application, we provide a rigorous mathematical …

An elementary approach to Gaussian multiplicative chaos

WebAug 25, 2024 · multiplicative chaos in number theory. This repository hosts code and data for the paper "A conjectural asymptotic formula for multiplicative chaos in number theory" by D. Aggarwal, U. Subedi, W. Verreault, A. Zaman, and C. Zheng. WebMar 25, 2024 · Gaussian free field, Liouville quantum gravity and Gaussian multiplicative chaos. These lecture notes are intended to be an introduction to the two-dimensional continuum Gaussian free field, Liouville quantum gravity and the general theory of Gaussian multiplicative chaos. Course Notes and Supplementary Material (PDF format) q tan optimista soy

Gaussian multiplicative chaos: applications and recent …

WebApr 9, 2024 · This is the first example of a non-Gaussian critical multiplicative chaos. We are inspired by methods coming from critical Gaussian multiplicative chaos, but there are essential differences, the main one being the lack of Gaussianity which prevents the use of Kahane’s inequality and hence a priori controls. Instead, a continuity lemma is ... WebMay 16, 2024 · The Lee–Yang property of certain moment generating functions having only pure imaginary zeros is valid for Ising type models with one-component spins and XY … WebThis demonstrates a novel rigorous connection between probabilistic number theory and the theory of multiplicative chaos—the latter is known to be connected to various branches of modern probability theory and mathematical physics. We also investigate the statistical behavior of the zeta function on the mesoscopic scale. q-ten japan

On Gaussian multiplicative chaos - ScienceDirect

WebMay 3, 2024 · In this paper we study imaginary Gaussian multiplicative chaos, formally written as \mu _\beta := :e^ {i\beta \Gamma (x)}:, where \Gamma is a log-correlated Gaussian field on a bounded domain U \subset {\mathbb {R}}^d and \beta a real parameter. WebJan 15, 2024 · The measure is constructed via a regularisation procedure, in which loops are killed at a fix rate, allowing us to make use of the Brownian multiplicative chaos measures previously considered in Aïdékon et al. (Ann. Probab. 48 (2024), no. 4, 1785–1825), Bass et al. (Ann. Probab. 22 (1994), no. 2, 566–625) and Jego (Ann. … haus tannaWebJun 22, 2024 · Gaussian multiplicative chaos: applications and recent developments Gaussian multiplicative chaos: applications and recent developments. I will give an introduction to Gaussian multiplicative chaos and some of its applications, e.g. in Liouville theory. Connections to random matrix theory and number theory will also be briefly … haus tannenkamp buch

"WebMay 25, 2024 · A completely elementary and self-contained proof of convergence of Gaussian multiplicative chaos is given. The argument shows further that the limiting random measure is nontrivial in the entire subcritical phase $(\gamma < \sqrt{2d} )$ and that the limit is universal (i.e., the limiting measure is independent of the regularisation of the … " - Gaussian multiplicative chaos

Gaussian multiplicative chaos

$Multifractal analysis of Gaussian multiplicative chaos and …$

WebMay 1, 2016 · The Gaussian multiplicative chaos (GMC) is the natural generalization of such a random measure to the setting when the field (X (t)) is defined in a distributional … WebJun 14, 2024 · Multifractal analysis of Gaussian multiplicative chaos and applications Federico Bertacco Let be a subcritical Gaussian multiplicative chaos measure associated with a general log-correlated Gaussian field defined on a bounded domain , .

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Web2 days ago · Given , we provide a construction of the random measure - the critical Gaussian Multiplicative Chaos - formally defined where is a -correlated Gaussian field and is a locally finite measure on . Our construction generalizes the one performed in the case where is the Lebesgue measure. It requires that the measure is sufficiently spread … Title: From Stochastic Integration wrt Fractional Brownian Motion to … In this article, we review the theory of Gaussian multiplicative chaos initially …

WebMay 13, 2024 · 3.1 Gaussian Multiplicative Chaos Measures. The foundations of the mathematical theory of Gaussian multiplicative chaos were established in the 1980s … WebJun 22, 2024 · Gaussian multiplicative chaos: applications and recent developments Gaussian multiplicative chaos: applications and recent developments. I will give an …

WebJun 6, 2024 · In this article we study imaginary Gaussian multiplicative chaos -- namely a family of random generalized functions which can formally be written as , where is a log-correlated real-valued Gaussian … WebJul 7, 2008 · In this article, we extend the theory of multiplicative chaos for positive definite functions in Rd of the form f(x) = 2 ln+ T x + g(x) where g is a continuous and bounded …

WebIntroduction to the Gaussian Free Field and Liouville Quantum Gravity (Berestycki) Polyakov's formulation of 2d Bosonic string theory (Guillarmou, Rhodes, Vargas) …

WebFeb 6, 2024 · Gaussian multiplicative chaos. The theory of Gaussian multiplicative chaos was initiated by Kahane [ 30 ] in an attempt to define rigorously a random measure of the form $e^{\alpha \phi (x)}\sigma (dx)$ where $\alpha >0$ is a real parameter, $\phi $ is a log-correlated, centered Gaussian field on a domain D and $\sigma $ is an ... haus tannenkamp instaWebMay 1, 2016 · The Gaussian multiplicative chaos (GMC) is the natural generalization of such a random measure to the setting when the field ( X ( t)) is defined in a distributional sense rather than pointwise, i.e. via a family of formal “integrals” against test functions from an appropriate class. haus tanneck kellenhusenWebLet M γ be a subcritical Gaussian multiplicative chaos measure associated with a general log-correlated Gaussian field defined on a bounded domain D ⊂ R d, d ≥ 1.We find an explicit formula for its singularity spectrum by showing that M γ satisfies almost surely the multifractal formalism, i.e., we prove that its singularity spectrum is almost surely equal to … haus tattooWebApr 15, 2024 · The dual neural network-based (DNN) k-winner-take-all (kWTA) model is one of the simplest analog neural network models for the kWTA process.This paper analyzes the behaviors of the DNN-kWTA model under these two imperfections.The two imperfections are, (1) the activation function of IO neurons is a logistic function rather than an ideal … haustarif fielmannWebMay 16, 2024 · Villain models and complex Gaussian multiplicative chaos are two-component systems analogous to XY models and related to Gaussian free fields. Although the Lee–Yang property is known to be valid generally … haus tanja syltWebFeb 7, 2024 · Universal tail profile of Gaussian multiplicative chaos SpringerLink Open Access Published: 07 February 2024 Universal tail profile of Gaussian multiplicative chaos Mo Dick Wong Probability Theory and Related Fields 177 , 711–746 ( 2024) Cite this article 1194 Accesses 4 Citations Metrics Reflection coefficient of GMC haus tannenkamp instagramWebJul 23, 2013 · In this article, we study complex Gaussian multiplicative chaos. More precisely, we study the renormalization theory and the limit of the exponential of a complex log-correlated Gaussian field in ... qtile on manjaro