scholarly journals Geometric density for invariant random subgroups of groups acting on CAT(0) spaces

2014 ◽  
Vol 175 (1) ◽  
pp. 249-256 ◽  
Author(s):  
Bruno Duchesne ◽  
Yair Glasner ◽  
Nir Lazarovich ◽  
Jean Lécureux
Keyword(s):  
Invariant Random Subgroups ◽  
Geometric Density

Infinitely presented permutation stable groups and invariant random subgroups of metabelian groups

2021 ◽  
pp. 1-36
Author(s):  
ARIE LEVIT ◽  
ALEXANDER LUBOTZKY
Keyword(s):  
Ergodic Theorem ◽  
Abelian Groups ◽  
Wreath Products ◽  
Finitely Generated ◽  
Metabelian Groups ◽  
Amenable Groups ◽  
Pointwise Ergodic Theorem ◽  
Lamplighter Group ◽  
Invariant Random Subgroups

Abstract We prove that all invariant random subgroups of the lamplighter group L are co-sofic. It follows that L is permutation stable, providing an example of an infinitely presented such group. Our proof applies more generally to all permutational wreath products of finitely generated abelian groups. We rely on the pointwise ergodic theorem for amenable groups.

Embedding Theorem for Inhomogeneous Besov and Triebel–Lizorkin Spaces on RD-spaces

2015 ◽  
Vol 58 (4) ◽  
pp. 757-773 ◽  
Author(s):  
Yanchang Han
Keyword(s):  
Embedding Theorem ◽  
Density Condition ◽  
Geometric Density

AbstractIn this article we prove an embedding theorem for inhomogeneous Besov and Triebel– Lizorkin spaces on RD-spaces. The crucial idea is to use the geometric density condition on the measure.

scholarly journals Invariant random subgroups of semidirect products

2018 ◽  
Vol 40 (2) ◽  
pp. 353-366
Author(s):  
IAN BIRINGER ◽  
LEWIS BOWEN ◽  
OMER TAMUZ
Keyword(s):  
Parabolic Subgroups ◽  
Semidirect Products ◽  
Invariant Random Subgroups

We study invariant random subgroups (IRSs) of semidirect products $G=A\rtimes \unicode[STIX]{x1D6E4}$. In particular, we characterize all IRSs of parabolic subgroups of $\text{SL}_{d}(\mathbb{R})$, and show that all ergodic IRSs of $\mathbb{R}^{d}\rtimes \text{SL}_{d}(\mathbb{R})$ are either of the form $\mathbb{R}^{d}\rtimes K$ for some IRS of $\text{SL}_{d}(\mathbb{R})$, or are induced from IRSs of $\unicode[STIX]{x1D6EC}\rtimes \text{SL}(\unicode[STIX]{x1D6EC})$, where $\unicode[STIX]{x1D6EC}<\mathbb{R}^{d}$ is a lattice.

Characters of inductive limits of finite alternating groups

2018 ◽  
Vol 40 (4) ◽  
pp. 1068-1082
Author(s):  
SIMON THOMAS
Keyword(s):  
Inductive Limit ◽  
Inductive Limits ◽  
Alternating Groups ◽  
Invariant Random Subgroups

If $G\ncong \operatorname{Alt}(\mathbb{N})$ is an inductive limit of finite alternating groups, then the indecomposable characters of $G$ are precisely the associated characters of the ergodic invariant random subgroups of $G$.

scholarly journals Smoothed particle magnetohydrodynamics with the geometric density average force expression

2020 ◽  
Vol 638 ◽  
pp. A140
Author(s):  
Robert Wissing ◽  
Sijing Shen
Keyword(s):  
Smoothed Particle Hydrodynamics ◽  
Weak Field ◽  
Average Force ◽  
Strong Discontinuities ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Novel Method ◽  
Mass Volume ◽  
Geometric Density ◽  
Do So

We present a novel method of magnetohydrodynamics (MHD) within the smoothed particle hydrodynamics scheme (SPMHD) using the geometric density average force expression. Geometric density average within smoothed particle hydrodynamics (GDSPH) has recently been shown to reduce the leading order errors and greatly improve the accuracy near density discontinuities, eliminating surface tension effects. Here, we extend the study to investigate how SPMHD benefits from this method. We implement ideal MHD in the GASOLINE2 and CHANGA codes with both GDSPH and traditional smoothed particle hydrodynamics (TSPH) schemes. A constrained hyperbolic divergence cleaning scheme was employed to control the divergence error and a switch for artificial resistivity with minimized dissipation was also used. We tested the codes with a large suite of MHD tests and showed that in all problems, the results are comparable or improved over previous SPMHD implementations. While both GDSPH and TSPH perform well with relatively smooth or highly supersonic flows, GDSPH shows significant improvements in the presence of strong discontinuities and large dynamic scales. In particular, when applied to the astrophysical problem of the collapse of a magnetized cloud, GDSPH realistically captures the development of a magnetic tower and jet launching in the weak-field regime, while exhibiting fast convergence with resolution, whereas TSPH failed to do so. Our new method shows qualitatively similar results to those of the meshless finite mass/volume schemes within the GIZMO code, while remaining computationally less expensive.

SUFFICIENT CONDITIONS FOR INTERPOLATION AND SAMPLING HYPERSURFACES IN THE BERGMAN BALL

2007 ◽  
Vol 18 (05) ◽  
pp. 559-584 ◽  
Author(s):  
TAMÁS FORGÁCS ◽  
DROR VAROLIN
Keyword(s):  
Recent Work ◽  
Fock Space ◽  
Sufficient Conditions ◽  
Higher Dimensions ◽  
Sampling Theorem ◽  
Interpolation Theorem ◽  
Smooth Hypersurface ◽  
Present Setting ◽  
Geometric Density ◽  
Natural Method

We give sufficient conditions for a closed smooth hypersurface W in the n-dimensional Bergman ball to be interpolating or sampling. As in the recent work [5] of Ortega-Cerdà, Schuster and the second author on the Bargmann–Fock space, our sufficient conditions are expressed in terms of a geometric density of the hypersurface that, though less natural, is shown to be equivalent to Bergman ball analogs of the Beurling-type densities used in [5]. In the interpolation theorem we interpolate L2 data from W to the ball using the method of Ohsawa–Takegoshi, extended to the present setting, rather than the Cousin I approach used in [5]. In the sampling theorem, our proof is completely different from [5]. We adapt the more natural method of Berndtsson and Ortega-Cerdà [1] to higher dimensions. This adaptation motivated the notion of density that we introduced. The approaches of [5] and the present paper both work in either the case of the Bergman ball or of the Bargmann–Fock space.

scholarly journals Invariant random subgroups over non-Archimedean local fields

2018 ◽  
Vol 372 (3-4) ◽  
pp. 1503-1544 ◽  
Author(s):  
Tsachik Gelander ◽  
Arie Levit
Keyword(s):  
Local Fields ◽  
Invariant Random Subgroups
Sign in / Sign up

Export Citation Format

Share Document