2 citations · 4 across the 10 of their papers we have counts for
11 papers
Small Kazhdan constants for small generating sets of linear groups
Tsachik Gelander, Alex Lubotzky, Jvbin Yao
Let G be a linear group with Kazhdan property (T) generated by d elements. We show that there are generating sets of size d+2 with arbitrarily small Kazhdan constants. We also prov…
Non Uniform Kazhdan Constant for Linear Groups
Alexander Lubotzky, Jvbin Yao
A group generated by a finite set has Property if the associated Kazhdan constant is positive. If so, the same holds for every finite generating set . The…
is flexibly stable in the operator norm
Alexander Lubotzky, Guy Salomon
A cornerstone of stability theory is Voiculescu's 1983 counterexample: he constructed a sequence of pairs of unitary matrices whose commutators converge to zero in the operator nor…
Subgroups with all finite lifts isomorphic are conjugate
Ido Karshon, Alexander Lubotzky, D. B. McReynolds +2
We show that for non-conjugate subgroups and of a finite group there exists an extension of (by a finite group) in which the pre-images of and are n…
On -approximation of groups
Benjamin Bachner, Alon Dogon, Alexander Lubotzky
A longstanding open problem in the intersection of group theory and operator algebras is whether all groups are MF, that is, approximated by asymptotic representations with respect…
Conditional Non-Soficity of p-adic Deligne Extensions: on a Theorem of Gohla and Thom
Michael Chapman, Yotam Dikstein, Alexander Lubotzky
A long standing problem asks whether every group is sofic, i.e., can be separated by almost-homomorphisms to the symmetric group . Similar problems have been asked with res…
The Aldous--Lyons Conjecture I: Subgroup Tests
Lewis Bowen, Michael Chapman, Alexander Lubotzky +1
This paper, and its companion [BCV24], are devoted to a negative resolution of the Aldous--Lyons Conjecture [AL07, Ald07]. This conjecture, originated in probability theory, is wel…
Non-commutative error correcting codes and proper subgroup testing
Michael Chapman, Irit Dinur, Alexander Lubotzky
Property testing has been a major area of research in computer science in the last three decades. By property testing we refer to an ensemble of problems, results and algorithms wh…
Low Acceptance Agreement Tests via Bounded-Degree Symplectic HDXs
Yotam Dikstein, Irit Dinur, Alexander Lubotzky
We solve the derandomized direct product testing question in the low acceptance regime, by constructing new high dimensional expanders that have no small connected covers. We show…
Stability of Homomorphisms, Coverings and Cocycles II: Examples, Applications and Open problems
Michael Chapman, Alexander Lubotzky
Coboundary expansion (with coefficients), and variations on it, have been the focus of intensive research in the last two decades. It was used to study random comple…
Stability of Homomorphisms, Coverings and Cocycles I: Equivalence
Michael Chapman, Alexander Lubotzky
This paper is motivated by recent developments in group stability, high dimensional expansion, local testability of error correcting codes and topological property testing. In Part…