作者：Corwin, Ivan; Ghosal, Promit; Hammond, Alan
作者单位：Columbia University; Massachusetts Institute of Technology (MIT); University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：We consider the narrow wedge solution to the Kardar-Parisi-Zhang stochastic PDE under the characteristic 3 : 2 : 1 scaling of time, space and fluctuations. We study the correlation of fluctuations at two different times. We show that, when the times are close to each other, the correlation approaches one at a power-law rate with exponent 2/3, while, when the two times are remote from each other, the correlation tends to zero at a powerlaw rate with exponent -1/3. We also prove exponential-type...
作者：Hough, Robert; Son, Hyojeong
作者单位：State University of New York (SUNY) System; Stony Brook University; Washington University (WUSTL)
摘要：Sandpile dynamics are considered on graphs constructed from periodic plane and space tilings by assigning a growing piece of the tiling, either torus or open boundary conditions. A general method of obtaining the Green's function of the tiling is given, and a total variation cut-off phenomenon is demonstrated under general conditions. It is shown that the boundary condition does not affect the mixing time for planar tilings. In a companion paper, computational methods are used to demonstrate t...
