100 research outputs found
Decorrelation of total mass via energy
The main result of this small note is a quantified version of the assertion
that if u and v solve two nonlinear stochastic heat equations, and if the
mutual energy between the initial states of the two stochastic PDEs is small,
then the total masses of the two systems are nearly uncorrelated for a very
long time. One of the consequences of this fact is that a stochastic heat
equation with regular coefficients is a finite system if and only if the
initial state is integrable
The dimension of the range of a transient random walk
We find formulas for the macroscopic Minkowski and Hausdorff dimensions of
the range of an arbitrary transient walk in Z^d. This endeavor solves a problem
of Barlow and Taylor (1991).Comment: 37 pages, 5 figure
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