17 citations · 31 across the 6 of their papers we have counts for
6 papers
Metastability in the dilute Ising model
T. Bodineau, B. Graham, M. Wouts
Consider Glauber dynamics for the Ising model on the hypercubic lattice with a positive magnetic field. Starting from the minus configuration, the system initially settles into a m…
Borel type bounds for the self-avoiding walk connective constant
B. T. Graham
Let be the self-avoiding walk connective constant on $\ZZ^d$. We show that the asymptotic expansion for in powers of satisfies Borel type bounds. This suppor…
Sublinear variance for directed last-passage percolation
B. T. Graham
A range of first-passage percolation type models are believed to demonstrate the related properties of sublinear variance and superdiffusivity. We show that directed last-passage p…
Sharp thresholds for the random-cluster and Ising models
Benjamin Graham, Geoffrey Grimmett
A sharp-threshold theorem is proved for box-crossing probabilities on the square lattice. The models in question are the random-cluster model near the self-dual point $p_{\mathrm {…
Rate of relaxation for a mean-field zero-range process
Benjamin T. Graham
We study the zero-range process on the complete graph. It is a Markov chain model for a microcanonical ensemble. We prove that the process converges to a fluid limit. The fluid lim…
Influence and sharp-threshold theorems for monotonic measures
B. T. Graham, G. R. Grimmett
The influence theorem for product measures on the discrete space {0,1}^N may be extended to probability measures with the property of monotonicity (which is equivalent to `strong p…