Related papers: Coupling methods for random topological Markov cha…
A coupling matrix technique is presented for the synthesis of nonreciprocal lossless two-port networks. This technique introduces complex inverters to build the nonreciprocal transversal network corresponding to the nonreciprocal coupling…
In this paper we study the spectral properties of Markov-operator on $L^{2}$-spaces. Lawler and Sokal (Trans. Amer. Math. Soc., 1988, 309, pp. 557-580) used isoperimetric constants for discrete and continuous time Markov chains to obtain a…
Many signals evolve in time as a stochastic process, randomly switching between states over discretely sampled time points. Here we make an explicit link between the underlying stochastic process of a signal that can take on a bounded…
Couplings play a central role in the analysis of Markov chain Monte Carlo algorithms and appear increasingly often in the algorithms themselves, e.g. in convergence diagnostics, parallelization, and variance reduction techniques. Existing…
A typical approach to analysing statistical properties of expanding maps is to show spectral gaps of associated transfer operators in adapted function spaces. The classical function spaces for this purpose are H\"older spaces and Sobolev…
Detecting anomalous edges in dynamic graphs is an important task in many applications over evolving triple-based data, such as social networks, transaction management, and epidemiology. A major challenge with this task is the absence of…
In this article we consider the Markovian products of invertible (not necessarily positive) matrices chosen from a strongly irreducible, contracting, finite set of matrices. We construct Markovian transfer operators and prove the spectral…
We introduce a novel percolation model that generalizes the classical Random Connection Model (RCM) to a random simplicial complex, allowing for a more refined understanding of connectivity and emergence of large-scale structures in random…
To a pair of subspaces wandering with respect to a row isometry we associate a transfer function which in general is multi-Toeplitz and in interesting special cases is multi-analytic. Then we describe in an expository way how characteristic…
Convergence diagnosis for Markov chain Monte Carlo is a matter of fundamental importance in computational statistics: it determines the resources allocated to a particular sampling problem and influences the practitioner's view of the…
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…
A random phase property establishing a link between quasi-one-dimensional random Schroedinger operators and full random matrix theory is advocated. Briefly summarized it states that the random transfer matrices placed into a normal system…
Robust estimates for the performance of complicated queueing networks can be obtained by showing that the number of jobs in the network is stochastically comparable to a simpler, analytically tractable reference network. Classical coupling…
We describe a scheme that enables a strong coherent coupling between a topological qubit and the quantized motion of a magnetized nanomechanical resonator. This coupling is achieved by attaching an array of magnetic tips to a namomechanical…
We introduce an ensemble Markov chain Monte Carlo approach to sampling from a probability density with known likelihood. This method upgrades an underlying Markov chain by allowing an ensemble of such chains to interact via a process in…
We report a new experimental approach using an optoelectronic feedback loop to investigate the dynamics of oscillators coupled on large complex networks with arbitrary topology. Our implementation is based on a single optoelectronic…
We provide a simplified proof of the existence, under some assumptions, of a spectral gap for the Perron-Frobenius operator of piecewise uniformly expanding maps on Riemannian manifolds when acting on some Sobolev spaces. Its consequences…
Random features (RFs) are a popular technique to scale up kernel methods in machine learning, replacing exact kernel evaluations with stochastic Monte Carlo estimates. They underpin models as diverse as efficient transformers (by…
Random unimodular lattice triangulations have been recently used as an embedded random graph model, which exhibit a crossover behaviour between an ordered, large-world and a disordered, small-world behaviour. Using the ergodic Pachner flips…
We propose to study unitary matrix ensembles defined in terms of unitary stochastic transition matrices associated with Markov processes on graphs. We argue that the spectral statistics of such an ensemble (after ensemble averaging) depends…