Random Functions via Dyson Brownian Motion: Progress and Problems

Abstract

We develope a computationally efficient extension of the Dyson Brownian Motion (DBM) algorithm to generate random function in C2 locally. We further explain that random functions generated via DBM show an unstable growth as the traversed distance increases. This feature restricts the use of such functions considerably if they are to be used to model globally defined ones. The latter is the case if one uses random functions to model landscapes in string theory. We provide a concrete example, based on a simple axionic potential often used in cosmology, to highlight this problem and also offer an ad hoc modification of DBM that suppresses this growth to some degree.

V3: typos corrected, conclusions unchanged; 13 pages, 4 figures

References in corpus (6)

• Axion Cosmology
• Natural and Multi-Natural Inflation in Axion Landscape
• Axion Landscape and Natural Inflation
• Charting an Inflationary Landscape with Random Matrix Theory
• Vacuum Selection on Axionic Landscapes
• Local random potentials of high differentiability to model the Landscape

Cited by in corpus (10)

• Adiabatic suppression of the axion abundance and isocurvature due to coupling to hidden monopoles
• Manyfield Inflation in Random Potentials
• Inflation in random Gaussian landscapes
• Inflation in Multi-field Modified DBM Potentials
• Inflation in multi-field random Gaussian landscapes
• Towards a complete mass spectrum of type-IIB flux vacua at large complex structure
• Learning to Inflate
• Inflation in Random Landscapes with two energy scales
• Local, algebraic simplifications of Gaussian random fields
• Efficient circular Dyson Brownian motion algorithm