TY - JOUR
T1 - Exact height distributions for the KPZ equation with narrow wedge initial condition
AU - Sasamoto, Tomohiro
AU - Spohn, Herbert
N1 - Funding Information:
We are grateful to Michael Prähofer for many illuminating discussions. H.S. thanks Jeremy Quastel for emphasizing the importance of the crossover WASEP. This work is supported by a DFG grant. In addition T.S. acknowledges the support from KAKENHI ( 9740044 ) and H.S. from Math-for-Industry of Kyushu University .
PY - 2010/8
Y1 - 2010/8
N2 - We consider the KPZ equation in one space dimension with narrow wedge initial condition, h(x,t=0)=-|x|/δ, δ≪1, evolving into a parabolic profile with superimposed fluctuations. Based on previous results for the weakly asymmetric simple exclusion process with step initial conditions, we obtain a determinantal formula for the one-point distribution of the solution h(x,t) valid for any x and t>0. The corresponding distribution function converges in the long time limit, t → ∞, to the Tracy-Widom distribution. The first order correction is a shift of order t-1/3. We provide numerical computations based on the exact formula.
AB - We consider the KPZ equation in one space dimension with narrow wedge initial condition, h(x,t=0)=-|x|/δ, δ≪1, evolving into a parabolic profile with superimposed fluctuations. Based on previous results for the weakly asymmetric simple exclusion process with step initial conditions, we obtain a determinantal formula for the one-point distribution of the solution h(x,t) valid for any x and t>0. The corresponding distribution function converges in the long time limit, t → ∞, to the Tracy-Widom distribution. The first order correction is a shift of order t-1/3. We provide numerical computations based on the exact formula.
UR - http://www.scopus.com/inward/record.url?scp=77952885302&partnerID=8YFLogxK
U2 - 10.1016/j.nuclphysb.2010.03.026
DO - 10.1016/j.nuclphysb.2010.03.026
M3 - Article
AN - SCOPUS:77952885302
SN - 0550-3213
VL - 834
SP - 523
EP - 542
JO - Nuclear Physics, Section B
JF - Nuclear Physics, Section B
IS - 3
ER -