Related papers: Approximate equivalence of actions

We give an alternative definition of relative hyperbolicity based on properties of closest-point projections on peripheral subgroups. We also derive a distance formula for relatively hyperbolic groups, similar to the one for mapping class…

An action of a compact quantum group on a compact metric space $(X,d)$ is (D)-isometric if the distance function is preserved by a diagonal action on $X\times X$. We show that an isometric action in this sense has the following additional…

In this paper we consider first order differential models of collective behaviors of groups of agents based on the mass conservation equation. Models are formulated taking the spatial distribution of the agents as the main unknown,…

Uncertainty relations are old, yet potentially rewarding to explore. By introducing a quantity called the uncertainty matrix, we provide a link between purity and observable incompatibility, and derive several stronger uncertainty relations…

We prove positive characteristic analogues of certain measure rigidity theorems in characteristic zero. More specifically we give a classification result for positive entropy measures on quotients of $\operatorname{SL}_d$ and a…

We show that probabilistic equivalence of a regret-based preference relationship over random variables is implied by a weak form of continuity and monotonicity.

Two measures of how near an arbitrary function between groups is to being a homomorphism are considered. These have properties similar to conjugates and commutators. The authors show that there is a rich theory based on these structures,…

We present an equivalence theorem to unify the two classes of uncertainty relations, i.e., the variance-based ones and the entropic forms, which shows that the entropy of an operator in a quantum system can be built from the variances of a…

Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and, as well as being fundamental to our understanding of quantum theory, they have practical applications such as for…

We establish rigidity for partial transformation groupoids associated with algebraic actions of semigroups: If two such groupoids (satisfying appropriate conditions) are isomorphic, then the globalizations of the initial algebraic actions…

Let $G$ be a sofic group, and let $\Sigma = (\sigma_n)_{n\geq 1}$ be a sofic approximation to it. For a probability-preserving $G$-system, a variant of the sofic entropy relative to $\Sigma$ has recently been defined in terms of sequences…

Consider homogeneous G/H and G/F, for an S-algebraic group G. A lattice {\Gamma} acts on the left strictly conservatively. The following rigidity results are obtained: morphisms, factors and joinings defined apriori only in the measurable…

We study smooth actions by lattices in higher-rank simple Lie groups. Assuming one element of the action acts with positive topological entropy, we prove a number of new rigidity results. For lattices in $\mathrm{SL}(n,\mathbb{R})$ acting…

Let $G$ be a connected Lie group and $\text{Sub}_G$ be the space of closed subgroups of $G$ equipped with the Chabauty topology. In this article, we investigate the existence of invariant random subgroups of $G$ supported on various orbits…

Symmetries concerning the ordinary coordinate spacetime and internal spacetime are discussed. A possible unification model of electroweak, strong and gravitational interactions is briefly described.

Let $\mathrm{Mod}(S_g)$ be the mapping class group of the closed orientable surface of genus $g \geq 2$. In this article, we derive necessary and sufficient conditions under which two torsion elements in $\mathrm{Mod}(S_g)$ will have…

We review computations of joint invariants on a linear symplectic space, discuss variations for an extension of group and space and relate this to other equivalence problems and approaches, most importantly to differential invariants.

We consider the logic space of countable (enumerated) groups and show that closed subspaces corresponding to some standard classes of groups have (do not have) generic groups. We also discuss the cases of semigroups and associative rings.

We derive and experimentally investigate a strong uncertainty relation valid for any $n$ unitary operators, which implies the standard uncertainty relation as a special case, and which can be written in terms of geometric phases. It is…

We prove that all (generalized) Higman groups on at least $5$ generators are superrigid for measure equivalence. More precisely, let $k\ge 5$, and let $H$ be a group with generators $a_1,\dots,a_k$, and Baumslag-Solitar relations given by…