Related papers: Combinatorics of cyclic-conditional freeness
Much of scientific data is collected as randomized experiments intervening on some and observing other variables of interest. Quite often, a given phenomenon is investigated in several studies, and different sets of variables are involved…
We introduce a theory of cyclic Kummer extensions of commutative rings for partial Galois extensions of finite groups, extending some of the well-known results of the theory of Kummer extensions of commutative rings developed by A. Z.…
We exhibit the invariance of cycle affinities in finite state Markov processes under various natural probabilistic constructions, for instance under conditioning and under a new combinatorial construction that we call ``drag and drop''. We…
We characterize the corings whose category of comodules has a generating set of small projective comodules in terms of the (non commutative) descent theory. In order to extricate the structure of these corings, we give a generalization of…
We develop a covariant kinetic theory for massive fermions in curved spacetime and external electromagnetic field based on quantum field theory. We derive four coupled semi-classical kinetic equations accurate at $O(\hbar)$, which describe…
In this paper, we develop the notion of free-Boolean independence in an amalgamation setting. We construct free-Boolean cumulants and show that the vanishing of mixed free-Boolean cumulants is equivalent to our free-Boolean independence…
In this paper, we study singular systems with complete sets of involutive constraints. The aim is to establish, within the Hamilton-Jacobi theory, the relationship between the Frobenius' theorem, the infinitesimal canonical transformations…
This paper is concerned with test of the conditional independence. We first establish an equivalence between the conditional independence and the mutual independence. Based on the equivalence, we propose an index to measure the conditional…
By way of Ziegler restrictions we study the relation between nearly free plane arrangements and combinatorics and we give a Yoshinaga-type criterion for plus-one generated plane arrangements.
We develop the theory of mixed finite elements in terms of special inverse systems of complexes of differential forms, defined over cellular complexes. Inclusion of cells corresponds to pullback of forms. The theory covers for instance…
In combinatorial topology we aim to triangulate manifolds such that their topological properties are reflected in the combinatorial structure of their description. Here, we give a combinatorial criterion on when exactly triangulations of…
We study the coefficients in the expansion of Jack polynomials in terms of power sums. We express them as polynomials in the free cumulants of the transition measure of an anisotropic Young diagram. We conjecture that such polynomials have…
We investigate the notion of quasi-invariant states introduced in [2, 3] from an analytic viewpoint.We give the structures of quasi-invariant states with uniformly bounded cocycles. As a consequence, we can apply a Theorem of Kovacs and…
Combinatory logic shows that bound variables can be eliminated without loss of expressiveness. It has applications both in the foundations of mathematics and in the implementation of functional programming languages. The original…
In this paper we continue the study of conditional Markov chains (CMCs) with finite state spaces, that we initiated in Bielecki, Jakubowski and Niew\k{e}g{\l}owski (2014a) in an effort to enrich the theory of CMCs that was originated in…
This paper derives a differential contraction condition for the existence of an orbitally-stable limit cycle in an autonomous system. This transverse contraction condition can be represented as a pointwise linear matrix inequality (LMI),…
We consider (self-adjoint) families of infinite matrices of noncommutative random variables such that the joint distribution of their entries is invariant under conjugation by a free quantum group. For the free orthogonal and…
We construct pairs of algebras with mixed independence relations by using truncations of reduced free products of algebras. For example, we construct free-Boolean pairs of algebras and free-monotone pairs of algebras. We also introduce…
We extend the theory of transience to general dynamical systems with no Markov structure assumed. This is linked to the theory of phase transitions. We also provide examples of new kinds of transient behaviour.
We summarize recent developments of the semiclassical description of shell effects in finite fermion systems with explicit inclusion of spin degrees of freedom, in particluar in the presence of spin-orbit interactions. We present a new…