On Riemann zeroes, Lognormal Multiplicative Chaos, and Selberg Integral

Abstract

Rescaled Mellin-type transforms of the exponential functional of the Bourgade-Kuan-Rodgers statistic of Riemann zeroes are conjecturally related to the distribution of the total mass of the limit lognormal stochastic measure of Mandelbrot-Bacry-Muzy. The conjecture implies that a non-trivial, log-infinitely divisible probability distribution is associated with Riemann zeroes. For application, integral moments, covariance structure, multiscaling spectrum, and asymptotics associated with the exponential functional are computed in closed form using the known meromorphic extension of the Selberg integral.

38 pages. To appear in Nonlinearity

References in corpus (5)

• Critical Gaussian multiplicative chaos: Convergence of the derivative martingale
• Freezing Transitions and Extreme Values: Random Matrix Theory, $\zeta (1/2+it)$, and Disordered Landscapes
• KPZ in one dimensional random geometry of multiplicative cascades
• High values of disorder-generated multifractals and logarithmically correlated processes
• Counting function fluctuations and extreme value threshold in multifractal patterns: the case study of an ideal $1/f$ noise

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• On Barnes Beta Distributions and Applications to the Maximum Distribution of the 2D Gaussian Free Field
• A Review of Conjectured Laws of Total Mass of Bacry-Muzy GMC Measures on the Interval and Circle and Their Applications
• One step replica symmetry breaking and extreme order statistics of logarithmic REMs
• Operator Product Expansion in Liouville Field Theory and Seiberg type transitions in log-correlated Random Energy Models
• Log-correlated Random Energy Models with extensive free energy fluctuations: pathologies caused by rare events as signatures of phase transitions
• A Theory of Intermittency Differentiation of 1D Infinitely Divisible Multiplicative Chaos Measures