Concentration of measure and mixing for Markov chains

We consider Markovian models on graphs with local dynamics. We show that, under suitable conditions, such Markov chains exhibit both rapid convergence to equilibrium and strong concentration of measure in the stationary distribution. We illustrate our results with applications to some known chains from computer science and statistical mechanics.Comment: 28 page

Risk management for traffic safety control

This paper offers a range of modelling ideas and techniques from mathematical statistics appropriate for analysing traffic accident data for the East region operation of CLP Power Hong Kong Limited and for the Hong Kong population in general. We further make proposals for alternative ways to record and collect data, and discuss ways to identify the major contributing factors behind accidents. We hope that our findings will enable the design of effective accident prevention strategies for CLP

On the maximum queue length in the supermarket model

There are $n$ queues, each with a single server. Customers arrive in a Poisson process at rate $\lambda n$, where $0<\lambda<1$. Upon arrival each customer selects $d\geq2$ servers uniformly at random, and joins the queue at a least-loaded server among those chosen. Service times are independent exponentially distributed random variables with mean 1. We show that the system is rapidly mixing, and then investigate the maximum length of a queue in the equilibrium distribution. We prove that with probability tending to 1 as $n\to\infty$ the maximum queue length takes at most two values, which are $\ln\ln n/\ln d+O(1)$.Comment: Published at http://dx.doi.org/10.1214/00911790500000710 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Entanglement in a three spin system controlled by electric and magnetic field

We show influence of electric field and magnetic flux on spin entanglement in an artificial triangular molecule build of coherently coupled quantum dots. In a subspace of doublet states an explicit relation of concurrence with spin correlation functions and chirality is presented. The electric field modifies super-exchange correlations, shifts many-electron levels (the Stark effect) as well as changes spin correlations. For some specific orientation of the electric field one can observe monogamy, for which one of the spins is separated from two others. Moreover, the Stark effect manifests itself in different spin entanglement for small and strong electric fields. A role of magnetic flux is opposite, it leads to circulation of spin supercurrents and spin delocalization.Comment: 7 pages, 8 figure