Related papers: A spectral property for concurrent systems and som…

We complexify a 1-d potential which exhibits bound, reflecting and free states to study various properties of a non-Hermitian system. This potential turns out a PT-symmetric non-Hermitian potential when one of the parameters becomes…

Probabilistic concurrent systems are foundational models for modern mobile computing. In this paper, a unifying approach to probabilistic testing equivalences is proposed. With the help of a new distribution-based semantics for…

To study the convergence to equilibrium in random maps we developed the spectral theory of the corresponding transfer (Perron-Frobenius) operators acting in a certain Banach space of generalized functions. The random maps under study in a…

The theory of quasirandomness has greatly expanded from its inaugural graph theoretical setting to several different combinatorial objects such as hypergraphs, tournaments, permutations, etc. However, these quasirandomness variants have…

The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity structure of its solutions. In particular, there is strong evidence that all integrable…

Correctness of concurrent objects is defined in terms of safety properties such as linearizability, sequential consistency, and quiescent consistency, and progress properties such as wait-, lock-, and obstruction-freedom. These properties,…

The recently established spectral Favard theorem for bounded banded matrices admitting a positive bidiagonal factorization is applied to a broader class of Markov chains with bounded banded transition matrices, extending beyond the…

Using spectral embedding based on the signless Laplacian, we obtain bounds on the spectrum of transition matrices on graphs. As a consequence, we bound return probabilities and the uniform mixing time of simple random walk on graphs. In…

The aim of this note is to present an elementary proof of a variation of Harris' ergodic theorem of Markov chains. This theorem, dating back to the fifties essentially states that a Markov chain is uniquely ergodic if it admits a ``small''…

In this note we prove a spectral gap for various Markov chains on various functional spaces. While proving that a spectral gap exists is relatively common, explicit estimates seems somewhat rare.These estimates are then used to apply the…

The problem of neutral fermions subject to an inversely linear potential is revisited. It is shown that an infinite set of bound-state solutions can be found on the condition that the fermion is embedded in an additional uniform background…

We study convergence properties of pseudo-marginal Markov chain Monte Carlo algorithms (Andrieu and Roberts [Ann. Statist. 37 (2009) 697-725]). We find that the asymptotic variance of the pseudo-marginal algorithm is always at least as…

We prove uniqueness problems for meromorphic inner functions on the upper half-plane. In these problems we consider spectral data depending partially or fully on the spectrum, derivative values at the spectrum, Clark measure or the spectrum…

Distribution testing is a fundamental statistical task with many applications, but we are interested in a variety of problems where systematic mislabelings of the sample prevent us from applying the existing theory. To apply distribution…

We prove an a priori lower bound for the pressure, or $p$-norm joint spectral radius, of a measure on the set of $d \times d$ real matrices which parallels a result of J. Bochi for the joint spectral radius. We apply this lower bound to…

We consider a non-relativistic quantum particle interacting with a singular potential supported by two parallel straight lines in the plane. We locate the essential spectrum under the hypothesis that the interaction asymptotically…

We investigate spectral properties of a quantum particle confined to an infinite straight planar strip by imposing Robin boundary conditions with variable coupling. Assuming that the coupling function tends to a constant at infinity, we…

This paper analyzes independence concepts for sets of probability measures associated with directed acyclic graphs. The paper shows that epistemic independence and the standard Markov condition violate desirable separation properties. The…

The paper is concerned with random $S$-adic systems arising from an i.i.d. sequence of unimodular substitutions. Using equidistribution results of Benoist and Quint, we show in Theorem 3.3 that, under some natural assumptions, if the…

We present a condition that guarantees spatially uniformity in the solution trajectories of a diffusively-coupled compartmental ODE model, where each compartment represents a spatial domain of components interconnected through diffusion…