For all TASEPs satisfying certain assumptions, we also prove the pointwise convergence of the kernels appearing in the joint distribution of particle positions to those appearing in the KPZ fixed point formula. Our result generalizes the result of Matetski, Quastel, and Remenik [18] in the ...
KPZ fixed pointLARGE TIME ASYMPTOTICSGROWTH-MODELSDISTRIBUTIONSPNGWe consider all totally asymmetric simple exclusion processes (TASEPs) whose transition probabilities are given by the Schutz-type formulas and which jump with homogeneous rates. We show that the multi-point distribution of particle ...
The KPZ fixed point is a (1+1)-dimensional space-time random field conjectured to be the universal limit for models within the Kardar-Parisi-Zhang (KPZ) universality class. We consider the KPZ fixed point with the narrow-wedge initial condition, conditioning on a large value at a specific ...
Convergence of exclusion processes and the KPZ equation to the KPZ fixed point We show that under the 1:2:3 scaling, critically probing large space and time, the height function of finite range asymmetric exclusion processes and the K... J Quastel,S Sarkar - 《Journal of the American Mathem...
The KPZ equation is a paradigmatic model in a class of models, known as the KPZ universality class, whose long-time limit is the KPZ fixed point. While this universality class is not strictly defined, all models in this class should share specific salient features. The KPZ equation itself ha...
BROWNIAN STRUCTURE IN THE KPZ FIXED POINT Our technique of proof harnesses a probabilistic resampling or Brownian Gibbs property satisfied by the Airy line ensemble after parabolic shift, and this ... J Calvert,A Hammond,M Hegde - 《Asterisque》 被引量: 0发表: 2023年 One-dimensional Kardar-Par...
One-sided reflected Brownian motions and the KPZ fixed point of exponential random walks, and converges in the 1:2:3 scaling limit to the KPZ fixed point, the scaling invariant Markov process defined in [MQR17]... M Nica,J Quastel,D Remenik - 《Arxiv》 被引量: 0发表: 2020年 Diffusio...
Nevertheless, the behavior is easily traced to the strong influence of the neighboring DP fixed point function. This note communicates, in part, unpublished work referenced in Phys. Rev. E58, R4096 (1998). We discovered, as well, that the RG road to asymptopia can be highly refined by ...
Equivalently, \bar{\lambda }(l) converges for l\rightarrow \infty (i.e. after all large wavenumber modes are eliminated) to a finite stable fixed point, the KPZ fixed point of the RG-flow. This fixed point is associated with the dynamical scaling exponent z=3/2. According to [40], ...
Furthermore, we have for any L\ge 1 fixed that \begin{aligned} \lim _{t\rightarrow \infty }{\mathbb {P}}(x_{t^{\delta /4}}^{1}(t-t^{\chi })\ge -t^{\delta })\le \lim _{t\rightarrow \infty } {\mathbb {P}}(x_{L}^{1}(t-t^{\chi })\ge -t^{\delta })=...