The boundary problem is considered for inhomogeneous increasing random walks on the square lattice ${\mathbb Z}_+^2$ with weighted edges. Explicit solutions are given for some instances related to the classical and generalized number triangles.
A q-analogue of de Finetti's theorem
$SLE_6$ and 2-d critical bond percolation on the square lattice
Operadic approach to Markov processes with boundaries on the square lattice in dimension 2 and larger
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