Related papers: Hyperlinear approximations to amenable groups come…
Let $H$ be an infinite dimensional separable Hilbert space, $B(H)$ the $C^*$-algebra of all bounded linear operators on $H,$ $U(B(H))$ the unitary group of $B(H)$ and ${\cal K}\subset B(H)$ the ideal of compact operators. Let $G$ be a…
We develop new tools in the theory of nonlinear random matrices and apply them to study the performance of the Sum of Squares (SoS) hierarchy on average-case problems. The SoS hierarchy is a powerful optimization technique that has achieved…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
This paper is a modified chapter of the author's Ph.D. thesis. We introduce the notions of sequentially approximated types and sequentially approximated Keisler measures. As the names imply, these are types which can be approximated by a…
We investigate properties of closed approximate subgroups of locally compact groups, with a particular interest for approximate lattices i.e. those approximate subgroups that are discrete and have finite co-volume. We prove an approximate…
We show that any pseudofinite group with NIP theory and with a finite upper bound on the length of chains of centralisers is soluble-by-finite. In particular, any NIP rosy pseudofinite group is soluble-by-finite. This generalises, and…
Explicit expressions for associated spherical functions of $SO(p,q)$ matrix groups are obtained using a generalized hypergeometric series of two variables.
We prove that amenability of a discrete group is equivalent to dimension flatness of certain ring inclusions naturally associated with measure preserving actions of the group. This provides a group-measure space theoretic solution to a…
We present an elementary description of sofic equivalence relations, as well as some permanence properties for soficity. We answer a question by Conley, Kechris and Tucker-Drob of determining soficity in terms of the full group for…
Averaging linear functional on the space continuous functions of the group of diffeomorphisms of interval is found. Amenability of several discrete subgroups of the group of diffeomorphisms $\Diff^3([0,1])$ of interval is prove. In…
Finding a non-sofic hyperbolic group will resolve two major problems in geometric group theory: Are there non sofic groups? Are there non residually finite hyperbolic groups? In this paper, we propose a new probabilistic approach to this…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…
When approximating elliptic problems by using specialized approximation techniques, we obtain large structured matrices whose analysis provides information on the stability of the method. Here we provide spectral and norm estimates for…
An approach is suggested defining effective sums of divergent series in the form of self-similar exponential approximants. The procedure of constructing these approximants from divergent series with arbitrary noninteger powers is developed.…
We prove that for an elementary amenable group, coherence of the group, homological coherence of the group, and coherence of the integral group ring are all equivalent. This generalises a result of Bieri and Strebel for finitely generated…
We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof…
Covariance representations are developed for the uniform distributions on the Euclidean spheres in terms of spherical gradients and Hessians. They are applied to derive a number of Sobolev type inequalities and to recover and refine the…
One often wishes for the ability to formally analyze large-scale systems---typically, however, one can either formally analyze a rather small system or informally analyze a large-scale system. This work tries to further close this…
A group is said to be strongly amenable if each of its proximal topological actions has a fixed point. We show that a finitely generated group is strongly amenable if and only if it is virtually nilpotent. More generally, a countable…