scholarly journals Higher Dimensional Lattice Walks: Connecting Combinatorial and Analytic Behavior

2019 ◽  
Vol 33 (4) ◽  
pp. 2140-2174 ◽  
Author(s):  
Stephen Melczer ◽  
Mark C. Wilson
Keyword(s):  
Dimensional Lattice ◽  
Higher Dimensional ◽  
Lattice Walks ◽  
Analytic Behavior

Existence of traveling wave solutions in nonlocal delayed higher-dimensional lattice systems with quasi-monotone nonlinearities

2021 ◽  
Vol 71 (6) ◽  
pp. 1459-1470
Author(s):  
Kun Li ◽  
Yanli He
Keyword(s):  
Traveling Wave ◽  
Solution Method ◽  
Traveling Wave Solutions ◽  
Lower Solution ◽  
Cooperative System ◽  
Lattice Systems ◽  
Dimensional Lattice ◽  
Wave Solutions ◽  
Higher Dimensional ◽  
Lower Solution Method

Abstract In this paper, we are concerned with the existence of traveling wave solutions in nonlocal delayed higher-dimensional lattice systems with quasi-monotone nonlinearities. By using the upper and lower solution method and Schauder’s fixed point theorem, we establish the existence of traveling wave solutions. To illustrate our results, the existence of traveling wave solutions for a nonlocal delayed higher-dimensional lattice cooperative system with two species are considered.

Three-Dimensional Lattice Walks in the Upper Half-Space: 10795

2001 ◽  
Vol 108 (10) ◽  
pp. 980 ◽  
Author(s):  
Emeric Deutsch ◽  
Jim Brawner
Keyword(s):  
Half Space ◽  
Three Dimensional ◽  
Dimensional Lattice ◽  
Lattice Walks

scholarly journals WILSON LOOPS IN 2D YANG-MILLS: EULER CHARACTERS AND LOOP EQUATIONS

1996 ◽  
Vol 11 (21) ◽  
pp. 3885-3933 ◽  
Author(s):  
SANJAYE RAMGOOLAM
Keyword(s):  
Lattice Models ◽  
Symmetric Groups ◽  
Linear Constraints ◽  
Partition Functions ◽  
Wilson Loops ◽  
Dimensional Lattice ◽  
Yang Mills ◽  
Branched Covering ◽  
Large N ◽  
Higher Dimensional

We give a simple diagrammatic algorithm for writing the chiral large N expansion of intersecting Wilson loops in 2D SU(N) and U(N) Yang-Mills theory in terms of symmetric groups, generalizing the result of Gross and Taylor for partition functions. We prove that these expansions compute Euler characters of a space of branched covering maps from string worldsheets with boundaries. We prove that the Migdal-Makeenko equations hold for the chiral theory and show that they can be expressed as linear constraints on perturbations of the chiral YM 2 partition functions. We briefly discuss finite N, the nonchiral expansion, and higher-dimensional lattice models.

scholarly journals Higher dimensional lattice paths with diagonal steps

1976 ◽  
Vol 15 (2) ◽  
pp. 137-140 ◽  
Author(s):  
B.R. Handa ◽  
S.G. Mohanty
Keyword(s):  
Lattice Paths ◽  
Dimensional Lattice ◽  
Higher Dimensional

scholarly journals Infinite Orders and Non-D-finite Property of 3-Dimensional Lattice Walks

10.37236/5408 ◽  
2016 ◽  
Vol 23 (3) ◽  
Author(s):  
Daniel K. Du ◽  
Qing-Hu Hou ◽  
Rong-Hua Wang
Keyword(s):  
Generating Function ◽  
Infinite Groups ◽  
Dimensional Lattice ◽  
3 Dimensional ◽  
Lattice Walks

Recently, Bostan and his coauthors investigated lattice walks restricted to the non-negative octant $\mathbb{N}^3$. For the $35548$ non-trivial models with at most six steps, they found that many models associated to a group of order at least $200$ and conjectured these groups were in fact infinite groups. In this paper, we first confirm these conjectures and then consider the non-$D$-finite property of the generating function for some of these models.

scholarly journals Continued Classification of 3D Lattice Models in the Positive Octant

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Axel Bacher ◽  
Manuel Kauers ◽  
Rika Yatchak
Keyword(s):  
Asymptotic Behaviour ◽  
Generating Function ◽  
Asymptotic Form ◽  
Three Dimensional ◽  
Lattice Models ◽  
Dimensional Lattice ◽  
Lattice Walks ◽  
Small Set ◽  
International Audience

International audience 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 from models for which there is no reason to expect that their generating function is D-finite, and we isolate a small set of models whose nature remains unclear and requires further investigation. For these, we give some experimental results about their asymptotic behaviour, based on the inspection of a large number of initial terms. At least for some of them, the guessed asymptotic form seems to tip the balance towards non-D-finiteness.

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