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The approximate uniform sampling of graph realizations with a given degree sequence is an everyday task in several social science, computer science, engineering etc. projects. One approach is using Markov chains. The best available current…
We develop a theory of operator renewal sequences in the context of infinite ergodic theory. For large classes of dynamical systems preserving an infinite measure, we determine the asymptotic behaviour of iterates $L^n$ of the transfer…
Let $P$ be a bistochastic matrix of size $n$, and let $\Pi$ be a permutation matrix of size $n$. In this paper, we are interested in the mixing time of the Markov chain whose transition matrix is given by $Q=P\Pi$. In other words, the chain…
We study pretty good quantum state transfer (i.e., state transfer that becomes arbitrarily close to perfect) between vertices of graphs with an involution in the presence of an energy potential. In particular, we show that if a graph has an…
This paper considers non-backtracking random walks on random graphs generated according to the configuration model. The quantity of interest is the scaling of the mixing time of the random walk as the number of vertices of the random graph…
We introduce novel finite element schemes for curve diffusion and elastic flow in arbitrary codimension. The schemes are based on a variational form of a system that includes a specifically chosen tangential motion. We derive optimal $L^2$-…
Nonlinear time series models with exogenous regressors are essential in econometrics, queuing theory, and machine learning, though their statistical analysis remains incomplete. Key results, such as the law of large numbers and the…
In this paper, based on a construction by J. Fickenscher, we construct a family of non-uniquely ergodic interval exchange transformations on $n$ intervals with the maximal possible number of measures, $\left\lfloor \frac{n}{2}…
We explore the distribution of paths followed in fluctuation-induced switching between coexisting stable states. We introduce a quantitative characteristic of the path distribution in phase space that does not require a priori knowledge of…
S=1/2 quantum spin chains and ladders with random exchange coupling are studied by using an effective low-energy field theory and transfer matrix methods. Effects of the nonlocal correlations of exchange couplings are investigated…
Wavelength-selective switches for mode-division-multiplexing systems are designed by scaling switches from single-mode systems. All modes at a given wavelength are switched as a unit, which is necessary in systems with substantial mode…
The topological transitions that occur to the grain boundary network during grain growth in a material with uniform grain boundary energies are believed to be known. The same is not true for more realistic materials, since more general…
A finite ergodic Markov chain is said to exhibit cutoff if its distance to stationarity remains close to 1 over a certain number of iterations and then abruptly drops to near 0 on a much shorter time scale. Discovered in the context of card…
We investigate two-dimensional Ising systems with multisping interactions of three- (m=3) and four-body terms (m=4). The application of a new type of finite-size algorithm of de Oliveira allow us to clearly distinguish a first-order…
This paper revisits the parametric analysis of semidefinite optimization problems with respect to the perturbation of the objective function along a fixed direction. We review the notions of invariancy set, nonlinearity interval, and…
Motivated by recent experimental advances (Stroock et al. 2002) in microfluidic mixers, we study the passive mixing and flow properties of a patterned microchannel by means of computational fluid dynamics (CFD). Such geometries overcome the…
Networks embedded in space can display all sorts of transitions when their structure is modified. The nature of these transitions (and in some cases crossovers) can differ from the usual appearance of a giant component as observed for the…
We analyze the so called Swapping Algorithm, a parallel version of the well-known Metropolis-Hastings algorithm, on the mean-field version of the Blume-Emery-Griffiths model in statistical mechanics. This model has two parameters and…
We present general results for one-dimensional systems of point charges (signed point measures) on the line with a translation invariant distribution $\mu$ for which the variance of the total charge in an interval is uniformly bounded…
We have studied numerically the random interchange model and related loop models on the three-dimensional cubic lattice. We have determined the transition time for the occurrence of long loops. The joint distribution of the lengths of long…