Apparent nonuniversality in finite segregated tunneling-percolaiton models

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Our motivation in this paper is twofold. First, we study the geometry of a class of exploration sets, called exit sets, which are naturally associated with a 2D vector-valued Gaussian Free Field:

\phi : \mathbb{Z}^2 \rightarrow \mathbb{R}^N

N \ge 1

. W ...

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In this thesis, we consider an anisotropic finite-range bond percolation model on

\mathbb{Z}^2

. On each horizontal layer

\{(x,i):x\in\mathbb{Z}\}

for

i\in\mathbb{Z}

, we have edges

\langle(x,i),(y,i)\rangle

for

1\leq|x-y|\leq N

with $N\in\mathbb{N ...

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Apparent nonuniversality in finite segregated tunneling-percolaiton models

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