Height Fluctuations for the Stationary KPZ Equation
By Alexei Borodin, Ivan Corwin, P. Ferrari, B. Vető. 2014
147 citations recorded by the source corpus.
We compute the one-point probability distribution for the stationary KPZ equation (i.e. initial data H(0,X)=B(X)$\mathcal {H}(0,X)=B(X)$, for B(X) a two-sided standard Brownian motion) and show that as time T goes to infinity, the fluctuations of the height function H(T,X)$\mathcal {H}(T,X)$ grow like T1/3 and converge to those previously encountered in the study of the stationary totally asymmetric simple exclusion process, polynuclear growth model and last passage percolation. The starting point for this work is our derivation of a Fredholm determinant formula for Macdonald processes which degenerates to a corresponding formula for Whittaker processes. We relate this to a polymer model which mixes the semi-discrete and log-gamma random polymers. A special case of this model has a limit to the KPZ equation with initial data given by a two-sided Brownian motion with drift ß to the left of the origin and b to the right of the origin. The Fredholm determinant has a limit for ß > b, and the case where ß = b (corresponding to the stationary initial data) follows from an analytic continuation argument.
Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/c03fc38e6dac5be17087cd2e19b91170792d7f2c
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In Condensed Matter Physics
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Citations in the corpus
- An appetizer to modern developments on the Kardar–Parisi–Zhang universality class (2017, background): “Now, there are a number of mathematical approaches to study the KPZ equation (a nice summary can be found in introduction of [55]), which have deepen the mathematical understanding of this equation even more.”