scholarly journals Convergence of ergodic averages on lattice random walks

1993 ◽  
Vol 37 (4) ◽  
pp. 624-636
Author(s):  
J. Bourgain
Keyword(s):  
Random Walks ◽  
Ergodic Averages ◽  
Lattice Random Walks

scholarly journals Multiphase partitions of lattice random walks

2019 ◽  
Vol 126 (5) ◽  
pp. 50002
Author(s):  
Massimiliano Giona ◽  
Davide Cocco
Keyword(s):  
Random Walks ◽  
Lattice Random Walks

scholarly journals Discrete Harmonic Functions in the Three-Quarter Plane

2021 ◽  
Author(s):  
Amélie Trotignon
Keyword(s):  
Functional Equation ◽  
Conformal Mapping ◽  
Boundary Value Problem ◽  
Random Walks ◽  
Harmonic Functions ◽  
Symmetric Convex ◽  
Planar Lattice ◽  
Quarter Plane ◽  
Lattice Random Walks ◽  
Discrete Harmonic Functions

AbstractIn this article we are interested in finding positive discrete harmonic functions with Dirichlet conditions in three quadrants. Whereas planar lattice (random) walks in the quadrant have been well studied, the case of walks avoiding a quadrant has been developed lately. We extend the method in the quarter plane—resolution of a functional equation via boundary value problem using a conformal mapping—to the three-quarter plane applying the strategy of splitting the domain into two symmetric convex cones. We obtain a simple explicit expression for the algebraic generating function of harmonic functions associated to random walks avoiding a quadrant.

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