Related papers: Representations of Aut(M)-Invariant Measures
In this paper, a decomposition theorem for (covariant) unitary group representations on Kaplansky-Hilbert modules over Stone algebras is established, which generalizes the well-known Hilbert space case (where it coincides with the…
We study a class of measure-theoretic objects that we call cubic couplings, on which there is a common generalization of the Gowers norms and the Host-Kra seminorms. Our main result yields a complete structural description of cubic…
This paper represents one approach to making explicit some of the assumptions and conditions implied in the widespread representation of numbers by composite quantum systems. Any nonempty set and associated operations is a set of natural…
Elements of a novel theory of quantum physics are developed, synthesising the role of symbolism in describing quantum measurement and in the topological representation of fractal invariant sets in nonlinear dynamical systems theory. In this…
Let $\mu$ be a probability measure (or corresponding random variable) such that all moments $\mu_n$ exist. Knowledge of the moments is not sufficient to determine infinite divisibility of the measure; we show also that infinitely divisible,…
We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint…
Measurement based (MB) quantum computation allows for universal quantum computing by measuring individual qubits prepared in entangled multipartite states, known as graph states. Unless corrected for, the randomness of the measurements…
We introduce the notion of coarse metric. Every coarse metric induces a coarse structure on the underlying set. Conversely, we observe that all coarse spaces come from a particular type of coarse metric in a unique way. In the case when the…
In this paper we prove a general form of the Mass Transference Principle for $\limsup$ sets defined via neighbourhoods of sets satisfying a certain local scaling property. Such sets include self-similar sets satisfying the open set…
Let $\Lambda$ be an isolated non-trival transitive set of a $C^1$ generic diffeomorphism $f\in\Diff(M)$. We show that the space of invariant measures supported on $\Lambda$ coincides with the space of accumulation measures of time averages…
A finitely-additive measure $\lambda $ on an infinite-dimensional real Hilbert space $E$ which is invariant with respect to shifts and orthogonal mappings has been defined. This measure can be considered as the analog of the Lebesgue…
For any countable group, and also for any locally compact second countable, compactly generated topological group, G, we show the existence of a "universal" hypercyclic (i.e. topologically transitive) representation on a Hilbert space, in…
We show that certain C*-algebras which have been studied among others by Arzumanian, Vershik, Deaconu, and Renault in connection to a measure preserving transformation of a measure space and/or to a covering map of a compact space are…
A Mauldin-Williams graph $\mathcal{M}$ is a generalization of an iterated function system by a directed graph. Its invariant set $K$ plays the role of the self-similar set. We associate a $C^{*}$-algebra $\mathcal{O}_{\mathcal{M}}(K)$ with…
Much of the work in loop quantum gravity and quantum geometry rests on a mathematically rigorous integration theory on spaces of distributional connections. Most notably, a diffeomorphism invariant representation of the algebra of basic…
Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of observables and of a representation of A on a measure space over the space of generalized connections. This representation is…
Let $\mathbf{K}$ be the class of countable structures $M$ with the strong small index property and locally finite algebraicity, and $\mathbf{K}_*$ the class of $M \in \mathbf{K}$ such that $acl_M(\{ a \}) = \{ a \}$ for every $a \in M$. For…
Singular statistical models arise whenever different parameter values induce the same distribution, leading to non-identifiability and a breakdown of classical asymptotic theory. While existing approaches analyze these phenomena in…
We initiate the effective metric structure theory of Keisler randomizations. We show that a classical countable structure $\mathcal{M}$ has a decidable presentation if and only if its Borel randomization $\mathcal{M}^{[0,1)}$ has a…
Given a preferred orthonormal basis $B$ in the Hilbert space of a quantum system we define a measure of the coherence generating power of a unitary operation with respect to $B$. This measure is the average coherence generated by the…