Tree lattice subgroups

2011 ◽  
Vol 3 (3) ◽  
pp. 1-23
Author(s):  
Lisa Carbone ◽  
Leigh Cobbs ◽  
Gabriel Rosenberg
Keyword(s):  
Tree Lattice ◽  
Lattice Subgroups

scholarly journals Orbit equivalence and rigidity of ergodic actions of Lie groups

1981 ◽  
Vol 1 (2) ◽  
pp. 237-253 ◽  
Author(s):  
Robert J. Zimmer
Keyword(s):  
Invariant Measure ◽  
Euclidean Space ◽  
Lie Groups ◽  
Homogeneous Spaces ◽  
The Other ◽  
Rigidity Theorem ◽  
Simple Groups ◽  
Orbit Equivalence ◽  
Finite Invariant Measure ◽  
Lattice Subgroups

AbstractThe rigidity theorem for ergodic actions of semi-simple groups and their lattice subgroups provides results concerning orbit equivalence of the actions of these groups with finite invariant measure. The main point of this paper is to extend the rigidity theorem on one hand to actions of general Lie groups with finite invariant measure, and on the other to actions of lattices on homogeneous spaces of the ambient connected group possibly without invariant measure. For example, this enables us to deduce non-orbit equivalence results for the actions of SL (n, ℤ) on projective space, Euclidean space, and general flag and Grassman varieties.

The tree lattice existence theorems

2002 ◽  
Vol 335 (3) ◽  
pp. 223-228 ◽  
Author(s):  
Lisa Carbone
Keyword(s):  
Existence Theorems ◽  
Tree Lattice

scholarly journals Stochastic bursting in networks of excitable units with delayed coupling

2021 ◽  
Author(s):  
Chunming Zheng ◽  
Arkady Pikovsky
Keyword(s):  
Spectral Density ◽  
Power Spectral Density ◽  
Directed Tree ◽  
Basic Assumptions ◽  
Delayed Coupling ◽  
Power Spectral ◽  
Delay Feedbacks ◽  
Cross Spectral Density ◽  
Tree Lattice ◽  
The One

AbstractWe investigate the phenomenon of stochastic bursting in a noisy excitable unit with multiple weak delay feedbacks, by virtue of a directed tree lattice model. We find statistical properties of the appearing sequence of spikes and expressions for the power spectral density. This simple model is extended to a network of three units with delayed coupling of a star type. We find the power spectral density of each unit and the cross-spectral density between any two units. The basic assumptions behind the analytical approach are the separation of timescales, allowing for a description of the spike train as a point process, and weakness of coupling, allowing for a representation of the action of overlapped spikes via the sum of the one-spike excitation probabilities.

scholarly journals Convex $L$-lattice subgroups in $L$-ordered groups

2018 ◽  
Vol 9 (1) ◽  
pp. 139-161 ◽  
Author(s):  
Rajabali Borzooei ◽  
Fateme Hosseini ◽  
Omid Zahiri
Keyword(s):  
Ordered Groups ◽  
Lattice Subgroups
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