9 citations · 11 across the 5 of their papers we have counts for
4 papers · 1 filter
The scaling limit of the weakly self-avoiding walk on a high-dimensional torus
Emmanuel Michta
We prove that the scaling limit of the weakly self-avoiding walk on a -dimensional discrete torus is Brownian motion on the continuum torus if the length of the rescaled walk is…
Weakly self-avoiding walk on a high-dimensional torus
Emmanuel Michta, Gordon Slade
How long does a self-avoiding walk on a discrete -dimensional torus have to be before it begins to behave differently from a self-avoiding walk on ? We consider a…
High-dimensional near-critical percolation and the torus plateau
Tom Hutchcroft, Emmanuel Michta, Gordon Slade
We consider percolation on and on the -dimensional discrete torus, in dimensions for the nearest-neighbour model and in dimensions for spread-out…
Asymptotic behaviour of the lattice Green function
Emmanuel Michta, Gordon Slade
The lattice Green function, i.e., the resolvent of the discrete Laplace operator, is fundamental in probability theory and mathematical physics. We derive its long-distance behavio…