Related papers: On distributional symmetries on the CAR algebra
Spreadability of a sequence of random variables is a distributional symmetry that is implemented by suitable actions of $\mathbb{J}_\mathbb{Z}$, the unital semigroup of strictly increasing maps on $\mathbb{Z}$ with cofinite range. We show…
We study characterization of separable (classically correlated) states for composite systems of distinguishable fermions that are represented as CAR algebras.
We characterize the finite distributive lattices on which there exists a unique compatible algebra with straightening laws.
We analyze general aspects of exchangeable quantum stochastic processes, as well as some concrete cases relevant for several applications to Quantum Physics and Probability. We establish that there is a one-to-one correspondence between…
We review old and new uses of exchangeability, emphasizing the general theme of exchangeable representations of complex random structures. Illustrations of this theme include processes of stochastic coalescence and fragmentation; continuum…
We consider quantum walks on the cycle in the non-stationary case where the `coin' operation is allowed to change at each time step. We characterize, in algebraic terms, the set of possible state transfers and prove that, as opposed to the…
We exhibit a family of *-isomorphisms mapping the CAR algebra onto its even subalgebra.
Iterative imputation, in which variables are imputed one at a time each given a model predicting from all the others, is a popular technique that can be convenient and flexible, as it replaces a potentially difficult multivariate modeling…
We show that the class of conditional distributions satisfying the coarsening at random (CAR) property for discrete data has a simple and robust algorithmic description based on randomized uniform multicovers: combinatorial objects…
In this note we identify the distributional limits of non-negative, ergodic stationary processes, showing that all are possible. Consequences for infinite ergodic theory are also explored and new examples of distributionally stable- and…
A relationally exchangeable structure is a random combinatorial structure whose law is invariant with respect to relabeling its relations, as opposed to its elements. Aside from exchangeable random partitions, examples include edge…
Currently there is great interest in computational models consisting of underlying regular computational environments, and built on them distributed computational structures. Examples of such models are cellular automata, spatial…
We show that the class of conditional distributions satisfying the coarsening at Random (CAR) property for discrete data has a simple and robust algorithmic description based on randomized uniform multicovers: combinatorial objects…
We study the independence structure of finitely exchangeable distributions over random vectors and random networks. In particular, we provide necessary and sufficient conditions for an exchangeable vector so that its elements are completely…
Using a complex parametrisation of $su(2)$, we show a change of coordinates that maps the maximally symmetric rolling $(2,3,5)$-distribution to the flat Cartan distribution. This establishes the local equivalence between the maximally…
We further study the stochastic model discussed in Ref.[2] in which positive and negative particles diffuse in an asymmetric, CP invariant way on a ring. The positive particles hop clockwise, the negative counter-clockwise and…
The stationary state of a stochastic process on a ring can be expressed using traces of monomials of an associative algebra defined by quadratic relations. If one considers only exclusion processes one can restrict the type of algebras and…
Entanglement sharing among sites of one-particle states is considered using the measure of concurrence. These are the simplest in an hierarchy of number-specific states of many qubits and corresponds to ``one-magnon'' states of spins. We…
Exchangeability is a central notion in statistics and probability theory. The assumption that an infinite sequence of data points is exchangeable is at the core of Bayesian statistics. However, finite exchangeability as a statistical…
It is shown how the theory of the fields can be constructed in a consistent way in quantized spaces. All constructions are connected with unitary irreducible representations of real forms of six dimensional rotation algebras O(1,5), O(2,4),…