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pro vyhledávání: '"Parkinson, J. A."'
We prove an analogue for homogeneous trees and certain affine buildings of a result of Bourgain on pinned distances in sets of positive density in Euclidean spaces. Furthermore, we construct an example of a non-homogeneous tree with positive Hausdorf
Externí odkaz:
http://arxiv.org/abs/1907.05825
Autor:
Parkinson, J.
Publikováno v:
London Mathematical Society Lecture Note Series, 436, 2017
In this paper we survey the theory of random walks on buildings and associated groups of Lie type and Kac-Moody groups. We begin with an introduction to the theory of Coxeter systems and buildings, taking a largely combinatorial perspective. We then
Externí odkaz:
http://arxiv.org/abs/1803.10880
Autor:
Guilhot, J., Parkinson, J.
We prove Lusztig's conjectures ${\bf P1}$-${\bf P15}$ for the affine Weyl group of type $\tilde{C}_2$ for all choices of positive weight function. Our approach to computing Lusztig's $\mathbf{a}$-function is based on the notion of a `balanced system
Externí odkaz:
http://arxiv.org/abs/1803.11067
Autor:
Parkinson, J., Van Maldeghem, H.
Publikováno v:
Innov. Incidence Geom. 17 (2019) 141-188
An automorphism $\theta$ of a spherical building $\Delta$ is called \textit{capped} if it satisfies the following property: if there exist both type $J_1$ and $J_2$ simplices of $\Delta$ mapped onto opposite simplices by $\theta$ then there exists a
Externí odkaz:
http://arxiv.org/abs/1803.09367
Autor:
Parkinson, J., Van Maldeghem, H.
Let $\theta$ be an automorphism of a thick irreducible spherical building $\Delta$ of rank at least $3$ with no Fano plane residues. We prove that if there exist both type $J_1$ and $J_2$ simplices of $\Delta$ mapped onto opposite simplices by $\thet
Externí odkaz:
http://arxiv.org/abs/1712.06094
Autor:
Guilhot, J., Parkinson, J.
We prove Lusztig's conjectures ${\bf P1}$--${\bf P15}$ for the affine Weyl group of type $\tilde{G}_2$ for all choices of parameters. Our approach to compute Lusztig's $\mathbf{a}$-function is based on the notion of a "balanced system of cell represe
Externí odkaz:
http://arxiv.org/abs/1711.06551
Autor:
Wijetunga, A., Jayamanne, D., Cook, R., Parkinson, J., Little, N., Curtis, J., Brown, C., Back, M.
Publikováno v:
In Journal of Clinical Neuroscience December 2020 82 Part A:155-161
In this paper we prove a rate of escape theorem and a central limit theorem for isotropic random walks on Fuchsian buildings, giving formulae for the speed and asymptotic variance. In particular, these results apply to random walks induced by bi-inva
Externí odkaz:
http://arxiv.org/abs/1411.7496
Publikováno v:
In Journal of Algebra 15 February 2019 520:460-478
Publikováno v:
In Journal of Environmental Management 15 June 2018 216:263-269