Related papers: On maximal agreement couplings
Classical coupling constructions arrange for copies of the \emph{same} Markov process started at two \emph{different} initial states to become equal as soon as possible. In this paper, we consider an alternative coupling framework in which…
Consider all the possible ways of coupling together two Brownian motions with the same starting position but with different drifts onto the same probability space. It is known that there exist couplings which make these processes agree for…
We generalize the optimal coupling theorem to multiple random variables: Given a collection of random variables, it is possible to couple all of them so that any two differ with probability comparable to the total-variation distance between…
The problem of maximizing (or minimizing) the agreement between clusterings, subject to given marginals, can be formally posed under a common framework for several agreement measures. Until now, it was possible to find its solution only…
The notion of a successful coupling of Markov processes, based on the idea that both components of the coupled system ``intersect'' in finite time with probability one, is extended to cover situations when the coupling is unnecessarily…
The coexistence of infinitely many attractors is called extreme multistability in dynamical systems. In coupled systems, this phenomenon is closely related to partial synchrony and characterized by the emergence of a conserved quantity. We…
This simple note lays out a few observations which are well known in many ways but may not have been said in quite this way before. The basic idea is that when comparing two different Markov chains it is useful to couple them is such a way…
Coupling is a widely used technique in the theoretical study of interacting stochastic processes. In this paper I present an example demonstrating its usefulness also in the efficient computer simulation of such processes. I first describe…
We consider a system of particles which interact through a jump process. The jump intensities are functions of the proximity rank of the particles, a type of interaction referred to as topological in the literature. Such interactions have…
Maximum bipartite matching is a fundamental algorithmic problem which can be solved in polynomial time. We consider a natural variant in which there is a separation constraint: the vertices on one side lie on a path or a grid, and two…
We consider a linear consensus system with n agents that can switch between r different connectivity patterns. A natural question is which switching law yields the best (or worst) possible speed of convergence to consensus? We formulate…
A dual control problem is presented for the optimal stochastic control of a system governed by partial differential equations. Relationships between the optimal values of the original and the dual problems are investigated and two duality…
The entanglement of superpositions [Phys. Rev. Lett. 97, 100502 (2006)] is generalized to the multipartite scenario: an upper bound to the multipartite entanglement of a superposition is given in terms of the entanglement of the superposed…
A compromise process describes the evolution of opinions through binary interactions. Opinions are real numbers, and at each step, two randomly selected agents reach a compromise by averaging their pre-interaction opinions. We prove that if…
Answering questions of Y. Rabinovich, we prove "stability" versions of upper bounds on maximal independent set counts in graphs under various restrictions. Roughly these say that being close to the maximum implies existence of a large…
An approach to analyse the properties of a particle system is to compare it with different processes to understand when one of them is larger than other ones. The main technique for that is coupling, which may not be easy to construct. We…
According to conventional wisdom, ambiguity accelerates optimal timing by decreasing the value of waiting in comparison with the unambiguous benchmark case. We study this mechanism in a multidimensional setting and show that in a…
The amount of correlation attainable between the components of a quantum system is constrained if the system is closed. We provide some examples, largely from the field of quantum thermodynamics, where knowing the maximal possible variation…
A measure of total correlations cannot increase under deterministic local operations. We show that, for any number of systems, this condition alone does not guarantee the existence of maximally correlated states. Namely, there is no state…
We provide analytical lower and upper bounds for entanglement of formation for bipartite systems, which give a direct relation between the bounds of entanglement of formation and concurrence, and improve the previous results. Detailed…