TY - JOUR
T1 - The one-dimensional KPZ equation and the Airy process
AU - Prolhac, Sylvain
AU - Spohn, Herbert
PY - 2011/3
Y1 - 2011/3
N2 - Our previous work on the one-dimensional KPZ equation with sharp wedge initial data is extended to the case of the joint height statistics at n spatial points for some common fixed time. Assuming a particular factorization, we compute an n-point generating function and write it in terms of a Fredholm determinant. For long times the generating function converges to a limit, which is established to be equivalent to the standard expression of the n-point distribution of the Airy process.
AB - Our previous work on the one-dimensional KPZ equation with sharp wedge initial data is extended to the case of the joint height statistics at n spatial points for some common fixed time. Assuming a particular factorization, we compute an n-point generating function and write it in terms of a Fredholm determinant. For long times the generating function converges to a limit, which is established to be equivalent to the standard expression of the n-point distribution of the Airy process.
KW - disordered systems (theory)
KW - quantum integrability (Bethe ansatz)
UR - http://www.scopus.com/inward/record.url?scp=79953704244&partnerID=8YFLogxK
U2 - 10.1088/1742-5468/2011/03/P03020
DO - 10.1088/1742-5468/2011/03/P03020
M3 - Article
AN - SCOPUS:79953704244
SN - 1742-5468
VL - 2011
JO - Journal of Statistical Mechanics: Theory and Experiment
JF - Journal of Statistical Mechanics: Theory and Experiment
IS - 3
M1 - P03020
ER -