Full asymptotic expansion for orbit-summable quadrant walks and discrete polyharmonic functions

Sums of independent random variables; random walks (60G50) Exact enumeration problems, generating functions (05A15) Harmonic functions on Riemann surfaces (30F15) Discrete potential theory (31C20)

Cites Work

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Asymptotic lattice path enumeration using diagonals
An elementary solution of Gessel's walks in the quadrant
Non-D-finite excursions in the quarter plane
On 3-dimensional lattice walks confined to the positive octant
Walks in the quarter plane: Kreweras' algebraic model
Hypergeometric expressions for generating functions of walks with small steps in the quarter plane
Square lattice walks avoiding a quadrant
Random walks in the quarter plane, discrete harmonic functions and conformal mappings
Two non-holonomic lattice walks in the quarter plane
Brownian motion in cones
On the arithmetical character of the coefficients of the substitutions of finite linear substitutions groups.
Basic analytic combinatorics of directed lattice paths
Automated positive part extraction for lattice path generating functions in the octant
On the functions counting walks with small steps in the quarter plane
Green functions for killed random walks in the Weyl chamber of \(\mathrm{Sp}(4)\)
Counting walks with large steps in an orthant
Discrete harmonic functions in the three-quarter plane
Walks in the quarter plane: genus zero case
Counting lattice walks by winding angle
On differentially algebraic generating series for walks in the quarter plane
About a possible analytic approach for walks in the quarter plane with arbitrary big jumps
On walks avoiding a quadrant
The kernel method for lattice paths below a line of rational slope
Random walks in cones
Weighted lattice walks and universality classes
Counting walks in a quadrant: a unified approach via boundary value problems
Walks with small steps in the 4D-orthant
Walks in the Quarter Plane with Multiple Steps
Random walks in the quarter plane with zero drift: an explicit criterion for the finiteness of the associated group
Some exact asymptotics in the counting of walks in the quarter-plane
Asymptotics for the number of walks in a Weyl chamber of typeB
Walks with small steps in the quarter plane
Two Parallel Queues Created by Arrivals with Two Demands I
The applications of harmonic functions to robotics
The complete generating function for Gessel walks is algebraic
Algorithmic and Symbolic Combinatorics
Constructing discrete harmonic functions in wedges
Higher Dimensional Lattice Walks: Connecting Combinatorial and Analytic Behavior
Enumeration of three-quadrant walks via invariants: some diagonally symmetric models
Polyharmonic Functions in the Quarter Plane