相关论文: On Kemeny's constant and stochastic complement

Starting from the $\kappa$-distribution function, obtained by applying the maximal entropy principle to the $\kappa$-entropy [G. Kaniadakis, Phys. Rev. E 66 (2002), 056125], we derive the expression of the canonical $\kappa$-partition…

We establish a second anti-blocker theorem for non-commutative convex corners, show that the anti-blocking operation is continuous on bounded sets of convex corners, and define optimisation parameters for a given convex corner that…

In this work we survey on connections of Markov chains and the theory of multiple orthogonality. Here we mainly concentrate on give a procedure to generate stochastic tetra diagonal Hessenberg matrices, coming from some specific families of…

In this paper, we delve into the study of the generalized KP equation, which incorporates double-power nonlinearities. Our investigation covers various aspects, including the existence of solitary waves, their nonlinear stability, and…

In the present effort we show that $S_{\kappa}=-k_B \int d^3p (n^{1+\kappa}-n^{1-\kappa})/(2\kappa)$ is the unique existing entropy obtained by a continuous deformation of the Shannon-Boltzmann entropy $S_0=-k_B \int d^3p n \ln n$ and…

We study Nordhaus-Gaddum problems for Kemeny's constant $\mathcal{K}(G)$ of a connected graph $G$. We prove bounds on $\min\{\mathcal{K}(G),\mathcal{K}(\overline{G})\}$ and the product $\mathcal{K}(G)\mathcal{K}(\overline{G})$ for various…

Multiplicative constants are a fundamental tool in the study of maximal representations. In this paper we show how to extend such notion, and the associated framework, to measurable cocycles theory. As an application of this approach, we…

In this paper we give a new sufficient condition for a general stability of Kronecker coefficients, which we call it additive stability. It was motivated by a recent talk of J. Stembridge at the conference in honor of Richard P. Stanley's…

We show that the Kottman constant $K(\cdot)$, together with its symmetric and finite variations, is continuous with respect to the Kadets metric, and they are log-convex, hence continuous, with respect to the interpolation parameter in a…

We construct quadratic stochastic processes (QSP) (also known as Markov processes of cubic matrices) in continuous and discrete times. These are dynamical systems given by (a fixed type, called $\sigma$) stochastic cubic matrices satisfying…

This paper elucidates the connection between the KS entropy-rate kappa and the time evolution of the physical or statistical entropy S. For a large family of chaotic conservative dynamical systems including the simplest ones, the evolution…

The equivalence of regularity of a Q-matrix with its bounded perturbations is proved and a integration by parts formula is established for the associated Feller minimal transition functions.

We consider the computational task of sampling a bit string $x$ from a distribution $\pi(x)=|\langle x|\psi\rangle|^2$, where $\psi$ is the unique ground state of a local Hamiltonian $H$. Our main result describes a direct link between the…

Given a diagonalizable matrix $A$, we study the stability of its invariant subspaces when its matrix of eigenvectors is ill-conditioned. Let $\mathcal{X}_1$ be some invariant subspace of $A$ and $X_1$ be the matrix storing the right…

Let $K$ be an algebraically closed field and $\mathrm{M}(2,K)$ be the $2\times 2$ matrix algebra over $K$ and $\mathrm{GL}(2,K)$ be the invertible elements in $\mathrm{M}(2,K)$. We explore the image of polynomials with constants, namely…

Real-valued triplet of scalar fields as source gives rise to a metric which tilts the scalar, not the light cone, in 2+1-dimensions. The topological metric is static, regular and it is characterized by an integer $\kappa =\pm 1,\pm 2,...$.…

We investigate the statistical stability of a class of dynamical systems semi-conjugate to pre-piecewise \textit{convex or expanding} maps with countably many branches. These systems naturally arise in the study of transformations with…

Kostka, Littlewood-Richardson, Kronecker, and plethysm coefficients are fundamental quantities in algebraic combinatorics, yet many natural questions about them stay unanswered for more than 80 years. Kronecker and plethysm coefficients…

A method for compression of large graphs and non-negative matrices to a block structure is proposed. Szemer\'edi's regularity lemma is used as heuristic motivation of the significance of stochastic block models. Another ingredient of the…

Let S be a denumerable state space and let P be a transition probability matrix on S. If a denumerable set M of nonnegative matrices is such that the sum of the matrices is equal to P, then we call M a partition of P. Let K denote the set…