2009/11/30 by Pavel Buividovich, P. V. Buividovich, Yuri Makeenko · 8 citations
Mathematics · Physics and Astronomy · #Computer network #Computer science #Mathematics #Path (computing) #Random Matrices and Applications #Random walk #Statistics #Stochastic processes and statistical mechanics #advanced mathematical theories #hep-lat #hep-th #math.PR
paper · pdf · doi:10.1016/j.nuclphysb.2010.03.003
published in Nuclear Physics B 834(3), 453-470 (Elsevier BV) · 22pp., RevTex, 9 figures; v2: sect.IV modified; v3: minor changes, to appear in Nucl. Phys. B
arxiv created 2010/03/09 · openalex publication_date 2010/03/09 · arxiv updated 2010/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate the properties of the path integral over reparametrizations (= the boundary value of the Liouville field in open string theory). Discretizing the path integral, we apply the Metropolis-Hastings algorithm to numerical simulations of a proper (subordinator) stochastic process and find that typical trajectories are not Brownian but rather have discontinuities of the type of Levy's flights. We study a fractal structure of these trajectories and show that their Hausdorff dimension is zero. We confirm thereby the discretization and heuristic consideration of QCD scattering amplitudes by analytical and numerical calculations. We also perform Monte Carlo simulations of the path integral over reparametrization in the effective-string ansatz for a circular Wilson loop and discuss their subtleties associated with the discretization of Douglas' functional.