High-precision simulation of the height distribution for the KPZ equation. (18th May 2018)

• Record Type: Journal Article
• Authors: Hartmann, Alexander K.; Le Doussal, Pierre; Majumdar, Satya N.; Rosso, Alberto; Schehr, Gregory
• Is Part Of: Europhysics letters. Volume 121:Number 6(2018:Mar.)
• Publication Date: 2018-05-18
• Subjects: 75.10.Nr -- 05.10.Ln -- 05.20.-y; Physics -- Periodicals; Electronic journals; 530.05
• DOI: 10.1209/0295-5075/121/67004
• Languages: English
• ISSNs: 0295-5075

Abstract

Abstract: The one-point distribution of the height for the continuum Kardar-Parisi-Zhang (KPZ) equation is determined numerically using the mapping to the directed polymer in a random potential at high temperature. Using an importance sampling approach, the distribution is obtained over a large range of values, down to a probability density as small as in the tails. Both short and long times are investigated and compared with recent analytical predictions for the large-deviation forms of the probability of rare fluctuations. At short times the agreement with the analytical expression is spectacular. We observe that the far left and right tails, with exponents 5/2 and 3/2, respectively, are preserved also in the region of long times. We present some evidence for the predicted non-trivial crossover in the left tail from the tail exponent to the cubic tail of the Tracy-Widom distribution, although the details of the full scaling form remain beyond reach.