Related papers: On a tracial version of Haemers bound

Hoffman's ratio bound is an upper bound for the independence number of a regular graph in terms of the eigenvalues of the adjacency matrix. The bound has proved to be very useful and has been applied many times. Hoffman did not publish his…

Connectivity is a fundamental property of quantum graphs, previously studied in the operator system model for matrix quantum graphs and via graph homomorphisms in the quantum adjacency matrix model. In this paper, we develop an algebraic…

We study the hard-core model defined on independent sets, where each independent set I in a graph G is weighted proportionally to $\lambda^{|I|}$, for a positive real parameter $\lambda$. For large $\lambda$, computing the partition…

Let $G_1 \times G_2$ denote the strong product of graphs $G_1$ and $G_2$, i.e. the graph on $V(G_1) \times V(G_2)$ in which $(u_1,u_2)$ and $(v_1,v_2)$ are adjacent if for each $i=1,2$ we have $u_i=v_i$ or $u_iv_i \in E(G_i)$. The Shannon…

Uniform continuity bounds on entropies are generally expressed in terms of a single distance measure between a pair of probability distributions or quantum states, typically, the total variation distance or trace distance. However, if an…

The notion of duality is a key element in understanding the interplay between the stability and chromatic numbers of a graph. This notion is a central aspect in the celebrated theory of perfect graphs, and is further and deeply developed in…

We consider periodic Schr\"{o}dinger operators on the hexagonal lattice with self-adjoint vertex conditions that allow discontinuity and concentrated mass at the vertices. This model generalizes the periodic Schr\"{o}dinger operator on the…

We define the notion of self-tracial stability for tracial von Neumann algebras and show that a tracial von Neumann algebra satisfying the Connes Embedding Problem is self-tracially stable if and only if it is amenable. We then generalize a…

The Vapnik-Chervonenkis dimension (in short, VC-dimension) of a graph is defined as the VC-dimension of the set system induced by the neighborhoods of its vertices. We show that every $n$-vertex graph with bounded VC-dimension contains a…

Recent progress in quantum field theory and quantum gravity relies on mixed boundary conditions involving both normal and tangential derivatives of the quantized field. In particular, the occurrence of tangential derivatives in the boundary…

We introduce an operator-algebraic framework for Morita equivalence of quantum graphs based on $\Delta$-equivalence of operator systems introduced by Eleftherakis, Kakariadis and Todorov. Adopting the perspective of Weaver, we view quantum…

In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of…

We present new degree-sequence lower bounds on the expected size of an independent set from the hard-core model. For arbitrary graphs, we establish a multivariate lower bound inspired by a conjecture of the first author and Kang and a…

In this paper we establish several invariant boundary versions of the (infinitesimal) Schwarz-Pick lemma for conformal pseudometrics on the unit disk and for holomorphic selfmaps of strongly convex domains in $\mathbb C^N$ in the spirit of…

As an analogue of the topological boundary of discrete groups $\Gamma$, we define the noncommutative topological boundary of tracial von Neumann algebras $(M, \tau)$ and apply it to generalize the main results of [AHO23], showing that for a…

We study upgraded free independence phenomena for unitary elements $u_1$, $u_2$, \dots representing the large-$n$ limit of Haar random unitaries, showing that free independence extends to several larger algebras containing $u_j$ in the…

We investigate quantum graphs with infinitely many vertices and edges without the common restriction on the geometry of the underlying metric graph that there is a positive lower bound on the lengths of its edges. Our central result is a…

Gromov's band-width conjecture gives a precise upper bound for the width of a compact Riemannian band with positive scalar curvature lower bound, assuming that the cross-section of the band admits no positive scalar curvature metrics.…

We establish uniform bounds on the multiplicities of irreducible admissible representations appearing in spaces of functions on symmetric spaces over $p$-adic fields. These multiplicities can exceed one and depend intricately on the group,…

We study singular integral operators induced by $3$-dimensional Calder\'on-Zygmund kernels in the Heisenberg group. We show that if such an operator is $L^{2}$ bounded on vertical planes, with uniform constants, then it is also $L^{2}$…