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We prove a number of results to the effect that generic quantum graphs (defined via operator systems as in the work of Duan-Severini-Winter / Weaver) have few symmetries: for a Zariski-dense open set of tuples $(X_1,cdots,X_d)$ of traceless self-adjoint operators in the $ntimes n$ matrix algebra the corresponding operator system has trivial automorphism group, in the largest possible range for the parameters: $2le dle n^2-3$. Moreover, the automorphism group is generically abelian in the larger parameter range $1le dle n^2-2$. This then implies that for those respective parameters the corresponding random-quantum-graph model built on the GUE ensembles of $X_i$s (mimicking the ErdH{o}s-R{e}nyi $G(n,p)$ model) has trivial/abelian automorphism group almost surely.
In this paper we define the notion of monic representation for the $C^*$-algebras of finite higher-rank graphs with no sources, and undertake a comprehensive study of them. Monic representations are the representations that, when restricted to the co
In this paper, we present a new way to associate a finitely summable spectral triple to a higher-rank graph $Lambda$, via the infinite path space $Lambda^infty$ of $Lambda$. Moreover, we prove that this spectral triple has a close connection to the w
Using coordinate-free basic operators on toy Fock spaces cite{AP}, quantum random walks are defined following the ideas in cite{LP,AP}. Strong convergence of quantum random walks associated with bounded structure maps is proved under suitable assumpt
We investigate the bottom of the spectra of infinite quantum graphs, i.e., Laplace operators on metric graphs having infinitely many edges and vertices. We introduce a new definition of the isoperimetric constant for quantum graphs and then prove the
Given a conditionally completely positive map $mathcal L$ on a unital $ast$-algebra $A$, we find an interesting connection between the second Hochschild cohomology of $A$ with coefficients in the bimodule $E_{mathcal L}=B^a(A oplus M)$ of adjointable