Gaussian multiplicative chaos
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. … 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 …
Gaussian multiplicative chaos
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WebJul 16, 2014 · Abstract: We propose a new definition of the Gaussian multiplicative chaos (GMC) and an approach based on the relation of subcritical GMC to randomized … 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.
WebJul 16, 2014 · We propose a new definition of the Gaussian multiplicative chaos (GMC) and an approach based on the relation of subcritical GMC to randomized shifts of a Gaussian measure. Using this relation we prove general uniqueness and convergence results for subcritical GMC that hold for Gaussian fields with arbitrary covariance … WebMay 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 …
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 … WebJul 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 ...
WebIntroduction to the Gaussian Free Field and Liouville Quantum Gravity (Berestycki) Polyakov's formulation of 2d Bosonic string theory (Guillarmou, Rhodes, Vargas) …
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. family x sWebMay 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. cooper instruments thermometersWeb2 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 … cooper institute standards chartWebRandom Hermitian matrices and Gaussian multiplicative chaos (with Christian Webb and Mo-Dick Wong). ( pdf) Probab. Theor. Rel. Fields, 172, 103-189 (2024). The Rohde-Schramm theorem, via the Gaussian free field (with Henry Jackson). ( pdf) Israel J. Math. , 228, 973-999 (2024). cooper insurance \u0026 associates incWebFeb 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 cooper insurance windsor ncWebOct 20, 2014 · Along the way we obtain general positive moment bounds for Gaussian multiplicative chaos. Contrary to previous results, this does not require any assumption on the underlying measure $\sigma$ such as scale invariance, and hence may be of independent interest. family x spy ep 5WebJun 24, 2024 · Gaussian Multiplicative Chaos is a way to produce a measure on R[superscript d] (or subdomain of R[superscript d]) of the form e[superscript γX(x)]dx, where X is a log-correlated Gaussian field ... cooper insurance revere ma