44 research outputs found
A note on weak convergence results for uniform infinite causal triangulations
We discuss uniform infinite causal triangulations and equivalence to the size
biased branching process measure - the critical Galton-Watson branching process
distribution conditioned on non-extinction. Using known results from the theory
of branching processes, this relation is used to prove weak convergence of the
joint length-area process of a uniform infinite causal triangulations to a
limiting diffusion. The diffusion equation enables us to determine the physical
Hamiltonian and Green's function from the Feynman-Kac procedure, providing us
with a mathematical rigorous proof of certain scaling limits of causal
dynamical triangulations.Comment: 23 pages, 2 figure
Repulsion of an evolving surface on walls with random heights
We consider the motion of a discrete random surface interacting by exclusion
with a random wall. The heights of the wall at the sites of are i.i.d.\
random variables. Fixed the wall configuration, the dynamics is given by the
serial harness process which is not allowed to go below the wall. We study the
effect of the distribution of the wall heights on the repulsion speed.Comment: 8 page