2019_EJRNL_PP_ABBAS_ALI_SABERI_1.pdf
Terbatas Ratnasari
» ITB
Terbatas Ratnasari
» ITB
We report on the universality of height fluctuations at the crossing point of two interacting (1 þ 1)-
dimensional Kardar-Parisi-Zhang interfaces with curved and flat initial conditions. We introduce a control
parameter p as the probability for the initially flat geometry to be chosen and compute the phase diagram as
a function of p. We find that the distribution of the fluctuations converges to the Gaussian orthogonal
ensemble Tracy-Widom distribution for p < 0.5, and to the Gaussian unitary ensemble Tracy-Widom
distribution for p > 0.5. For p ¼ 0.5 where the two geometries are equally weighted, the behavior is
governed by an emergent Gaussian statistics in the universality class of Brownian motion. We propose a
phenomenological theory to explain our findings and discuss possible applications in nonequilibrium
transport and traffic flow.