Related papers: Free evolution on algebras with two states
In this paper, we give a description of polynomial functors from (finitely generated free) groups to abelian groups in terms of non-linear Mackey functors generalizing those given in a paper of Baues-Dreckmann-Franjou-Pirashvili published…
We consider a macroscopic quantum system with unitarily evolving pure state $\psi_t\in \mathcal{H}$ and take it for granted that different macro states correspond to mutually orthogonal, high-dimensional subspaces $\mathcal{H}_\nu$ (macro…
In \cite{cartier2}, Pierre Cartier conjectured that for any non commutative formal power series $\Phi$ on $X=\{x_0,x_1\}$ with coefficients in a $\Q$-extension, $A$, subjected to some suitable conditions, there exists an unique algebra…
One of the main applications of free probability is to show that for appropriately chosen independent copies of $d$ random matrix models, any noncommutative polynomial in these $d$ variables has a spectral distribution that converges…
The purpose of the present paper is twofold. In the first part, we provide an algebraic characterization of several families of $\nu= \frac{1}{2^n}$ $n\leq 5$ BPS states in M theory, at threshold and non-threshold, by an analysis of the BPS…
We study the Hopf algebra of double posets and two of its Hopf subalgebras, the Hopf algebras of plane posets and of posets "without N". We prove that they are free, cofree, self-dual, and we give an explicit Hopf pairing on these Hopf…
Over an arbitrary field $\mathbb{F}$, let $p$ and $q$ be monic polynomials with degree $2$ in $\mathbb{F}[t]$. The free Hamilton algebra of the pair $(p,q)$ is the free noncommutative algebra in two generators $a$ and $b$ subject only to…
Assume that a basic algebra $A$ over an algebraically closed field $\Bbbk$ with a basic set $A_0$ of primitive idempotents has the property that $eAe=\Bbbk$ for all $e \in A_0$. Let $n$ be a nonzero integer, and $\phi$ and $\psi$ two…
Ziegler showed that free arrangements have free restricted multiarrangements (multirestrictions). After Ziegler's work, several results concerning "reverse direction", namely characterizing freeness of an arrangement via that of…
We consider absolutely free nonassociative algebras and, more generally, absolutely free algebras with (maybe infinitely) many multilinear operations. Such algebras are described in terms of labeled reduced planar rooted trees. This allows…
Starting from context-free inverse graphs, we introduce a new class of groups and study their structural properties. We establish closure properties, show that their co-word problems are context-free, analyze torsion elements, and realize…
A dynamical picture of phylogenetic evolution is given in terms of Markov models on a state space, comprising joint probability distributions for character types of taxonomic classes. Phylogenetic branching is a process which augments the…
We extend the polynomial method of Chen--Garza-Vargas--Tropp--van Handel and Magee--Puder--van Handel for operator-norm bounds in random permutation models to the setting where torsion is present. The main new feature is that asymptotic…
The generalization of the concept of interaction-free evolutions (IFE) [A. Napoli, {\it et al.}, Phys. Rev. A {\bf 89}, 062104 (2014)] to the case of time-dependent Hamiltonians is discussed. It turns out that the time-dependent case allows…
The functional equation defining the free cumulants in free probability is lifted successively to the noncommutative Fa\`a di Bruno algebra, and then to the group of a free operad over Schr\"oder trees. This leads to new combinatorial…
We investigate variance bounds under symmetry constraints in classical, free, and Boolean probability, focusing on Bernoulli distributions and their noncommutative analogues, projections with trace \(p\). We show that symmetrizers under…
The paper is devoted to infinite Bernoulli convolutions generated by positive multigeometric series and to probability distributions of random variables whose digits in an even integer base-$s$ expansion with two redundant digits form a…
In discrete contexts such as the degree distribution for a graph, \emph{scale-free} has traditionally been \emph{defined} to be \emph{power-law}. We propose a reasonable interpretation of \emph{scale-free}, namely, invariance under the…
In this article, we show that a technique for showing well-posedness results for evolutionary equations in the sense of [13] established in [16] applies to a broader class of non-autonomous integro-differential-algebraic equations. Using…
Let $W$ be a differential (not necessarily commutative) algebra which carries a free action of a polynomial algebra $SP$ with homogeneous generators $p_1, >..., p_r$. We show that for $W$ acyclic, the cohomology of the quotient $H(W/<p_1,…