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Free boundary dimers: random walk representation and scaling limit
Nathanael Berestycki, Marcin Lis, Wei Qian
We study the dimer model on subgraphs of the square lattice in which vertices on a prescribed part of the boundary (the free boundary) are possibly unmatched. Each such unmatched v…
On delocalization in the six-vertex model
Marcin Lis
We show that the six-vertex model with parameter on a square lattice torus has an ergodic infinite-volume limit as the size of the torus grows to infinity. Moreo…
Spins, percolation and height functions
Marcin Lis
To highlight certain similarities in combinatorial representations of several well known two-dimensional models of statistical mechanics, we introduce and study a new family of mod…
Gaussian approximation of moments of sums of independent random variables
Marcin Lis
We continue the research of Latała on improving estimates of -th moments of sums of independent random variables. We generalize some of his results in the case when $2 \leq p \l…