scholarly journals Strong relative property (T) and spectral gap of random walks

2012 ◽  
Vol 164 (1) ◽  
pp. 9-25
Author(s):  
C. R. E. Raja
Keyword(s):  
Random Walks ◽  
Spectral Gap ◽  
Relative Property ◽  
Property T

scholarly journals A Spectral Gap Property for Random Walks Under Unitary Representations

2006 ◽  
Vol 118 (1) ◽  
pp. 141-155 ◽  
Author(s):  
Bachir Bekka ◽  
Yves Guivarc’h
Keyword(s):  
Random Walks ◽  
Spectral Gap ◽  
Unitary Representations

scholarly journals On relative property (T) and Haagerup’s property

2011 ◽  
Vol 363 (12) ◽  
pp. 6407-6420 ◽  
Author(s):  
Ionut Chifan ◽  
Adrian Ioana
Keyword(s):  
Relative Property ◽  
Property T

scholarly journals COARSE EMBEDDINGS INTO A HILBERT SPACE, HAAGERUP PROPERTY AND POINCARÉ INEQUALITIES

2009 ◽  
Vol 01 (01) ◽  
pp. 87-100 ◽  
Author(s):  
ROMAIN TESSERA
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Metric Space ◽  
Unitary Representations ◽  
Poincaré Inequalities ◽  
Haagerup Property ◽  
Relative Property ◽  
Poincare Inequalities ◽  
Isometric Actions ◽  
Property T

We prove that a metric space does not coarsely embed into a Hilbert space if and only if it satisfies a sequence of Poincaré inequalities, which can be formulated in terms of (generalized) expanders. We also give quantitative statements, relative to the compression. In the equivariant context, our result says that a group does not have the Haagerup Property if and only if it has relative property T with respect to a family of probabilities whose supports go to infinity. We give versions of this result both in terms of unitary representations, and in terms of affine isometric actions on Hilbert spaces.

scholarly journals Stable laws and spectral gap properties for affine random walks

2015 ◽  
Vol 51 (1) ◽  
pp. 319-348
Author(s):  
Zhiqiang Gao ◽  
Yves Guivarc’h ◽  
Émile Le Page
Keyword(s):  
Random Walks ◽  
Spectral Gap ◽  
Stable Laws

Borel cocycles, approximation properties and relative property T

2000 ◽  
Vol 20 (2) ◽  
pp. 483-499 ◽  
Author(s):  
PAUL JOLISSAINT
Keyword(s):  
Von Neumann Algebra ◽  
Approximation Property ◽  
Compact Groups ◽  
Approximation Properties ◽  
Von Neumann ◽  
Rigidity Results ◽  
Relative Property ◽  
Finite Von Neumann Algebra ◽  
Property T ◽  
Standard Probability

Let $G$ and $H$ be locally compact groups. Assume that $G$ acts on a standard probability space $(S,\mu)$, $\mu$ being $G$-invariant. We prove that if there exists a Borel cocycle $\alpha:S\times G\longrightarrow H$ which is proper in an appropriate sense, then $G$ inherits some approximation properties of $H$, for instance amenability or the so-called Haagerup Approximation Property. On the other hand, if $G_{0}$ is a closed subgroup of $G$, if the pair $(G,G_{0})$ has the relative property (T) of Margulis [19] and if either $H$ has Haagerup Approximation Property, or if it is the unitary group of a finite von Neumann algebra with a similar property, then we give rigidity results analogous to that in [23] and [1].

scholarly journals High Order Random Walks: Beyond Spectral Gap

COMBINATORICA ◽  
2020 ◽  
Vol 40 (2) ◽  
pp. 245-281
Author(s):  
Tali Kaufman ◽  
Izhar Oppenheim
Keyword(s):  
Random Walks ◽  
Spectral Gap ◽  
High Order

scholarly journals Relative Inner Amenability and Relative Property Gamma

2016 ◽  
Vol 119 (2) ◽  
pp. 293
Author(s):  
Paul Jolissaint
Keyword(s):  
Discrete Group ◽  
Proper Subgroup ◽  
Type Ii ◽  
Semidirect Products ◽  
Relative Property ◽  
Property T ◽  
Equivalent Conditions ◽  
Inner Amenability

Let $H$ be a proper subgroup of a discrete group $G$. We introduce a notion of relative inner amenability of $H$ in $G$, we prove some equivalent conditions and provide examples coming mainly from semidirect products, as well as counter-examples. We also discuss the corresponding relative property gamma for pairs of type II$_1$ factors $N\subset M$ and we deduce from this a characterization of discrete, icc groups which do not have property (T).

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