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math.PR2025
Boundary contacts for reflected random walks in the quarter plane
Viet Hung Hoang, Kilian Raschel
We investigate reflected random walks in the quarter plane, with particular emphasis on the time spent along the reflection boundary axes. Assuming the drift of the random walk lie…
math.PR2022
Harmonic functions for singular quadrant walks
Viet Hung Hoang, Kilian Raschel, Pierre Tarrago
We consider discrete (time and space) random walks confined to the quarter plane, with jumps only in directions with and small negative jumps, i.e., $i,j \geq…
math.PR2022★ 2 cited
Discrete harmonic functions for non-symmetric Laplace operators in the quarter plane
Viet Hung Hoang
We construct harmonic functions in the quarter plane for discrete Laplace operators. In particular, the functions are conditioned to vanish on the boundary and the Laplacians admit…