[HTML][HTML] Non-D-finite excursions in the quarter plane
The number of excursions (finite paths starting and ending at the origin) having a given
number of steps and obeying various geometric constraints is a classical topic of …
number of steps and obeying various geometric constraints is a classical topic of …
Counting walks with large steps in an orthant
Counting walks with large steps in an orthant Page 1 © 2021 European Mathematical
Society Published by EMS Press. This work is licensed under a CC BY 4.0 license. J. Eur …
Society Published by EMS Press. This work is licensed under a CC BY 4.0 license. J. Eur …
Singularity analysis via the iterated kernel method
In the quarter plane, five lattice path models with unit steps have resisted the otherwise
general approach featured in recent works by Fayolle, Kurkova and Raschel. Here we …
general approach featured in recent works by Fayolle, Kurkova and Raschel. Here we …
Logarithmic terms in discrete heat kernel expansions in the quadrant
A Elvey-Price, A Nessmann, K Raschel - arXiv preprint arXiv:2309.15209, 2023 - arxiv.org
In the context of lattice walk enumeration in cones, we consider the number of walks in the
quarter plane with fixed starting and ending points, prescribed step-set and given length …
quarter plane with fixed starting and ending points, prescribed step-set and given length …
On the exit time from a cone for random walks with drift
R Garbit, K Raschel - Revista Matematica Iberoamericana, 2016 - ems.press
We compute the exponential decay of the probability that a given multi-dimensional random
walk stays in a convex cone up to time n, as n goes to infinity. We show that the latter equals …
walk stays in a convex cone up to time n, as n goes to infinity. We show that the latter equals …
Logarithmic terms in discrete heat kernel expansions in the quadrant
AE Price, A Nessmann, K Raschel - Annales de l'Institut Henri Poincaré …, 2024 - ems.press
In the context of lattice walk enumeration in cones, we consider the number of walks in the
quarter plane with fixed starting and ending points, prescribed step-set, and given length …
quarter plane with fixed starting and ending points, prescribed step-set, and given length …
Continued classification of 3D lattice models in the positive octant
A Bacher, M Kauers, R Yatchak - Discrete Mathematics & …, 2020 - dmtcs.episciences.org
We continue the investigations of lattice walks in the three-dimensional lattice restricted to
the positive octant. We separate models which clearly have a D-finite generating function …
the positive octant. We separate models which clearly have a D-finite generating function …
Occupation times and areas derived from random sampling
F Aurzada, L Döring, HH Pitters - arXiv preprint arXiv:2406.09886, 2024 - arxiv.org
We consider the occupation area of spherical (fractional) Brownian motion, ie the area
where the process is positive, and show that it is uniformly distributed. For the proof, we …
where the process is positive, and show that it is uniformly distributed. For the proof, we …
Uniform Sampling and Visualization of 3D Reluctant Walks
B Buckley, M Mishna - arXiv preprint arXiv:2406.16397, 2024 - arxiv.org
A family of walks confined to the first orthant whose defining stepset has drift outside of the
region can be challenging to sample uniformly at random for large lengths. We address this …
region can be challenging to sample uniformly at random for large lengths. We address this …
Computer algebra for lattice path combinatorics
A Bostan - 2017 - hal.science
Classifying lattice walks in restricted lattices is an important problem in enumerative
combinatorics. Recently, computer algebra has been used to explore and to solve a number …
combinatorics. Recently, computer algebra has been used to explore and to solve a number …