Linearly edge-reinforced random walks

We review results on linearly edge-reinforced random walks. On finite graphs, the process has the same distribution as a mixture of reversible Markov chains. This has applications in Bayesian statistics and it has been used in studying the random walk on infinite graphs. On trees, one has a representation as a random walk in an independent random environment. We review recent results for the random walk on ladders: recurrence, a representation as a random walk in a random environment, and estimates for the position of the random walker.Comment: Published at http://dx.doi.org/10.1214/074921706000000103 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Synthesis of polyethers of hexafluorobenzene and hexafluoropentanediol

Two new polyethers, poly /hexafluoropentamethylene tetrafluoro-p-phenylene ether/ and a completely hydroxyl-terminated polyether, is prepared by reactions of hexafluorobenzene with hexafluoropentanediol. The polyethers can be prepared as low molecular weight oils, as intermediate molecular weight waxes, or as high molecular weight elastomers

Purification of quantum trajectories

We prove that the quantum trajectory of repeated perfect measurement on a finite quantum system either asymptotically purifies, or hits upon a family of `dark' subspaces, where the time evolution is unitary.Comment: 10 page

The development of structural adhesive systems suitable for use with liquid oxygen Annual summary report, 1 Jul. 1964 - 30 Jun. 1965

Preparation and testing of adhesive polyurethanes, polycarbonates, and other highy halogenated polymers for liquid oxygen compatibilit

The development of structural adhesives systems suitable for use with liquid oxygen Annual summary report, 1 Jul. 1963 - 30 Jun. 1964

Fluorinated, chlorinated, and halogenated polymer adhesives prepared and tested for compatibility with liquid oxyge

Measuring degree-degree association in networks

The Pearson correlation coefficient is commonly used for quantifying the global level of degree-degree association in complex networks. Here, we use a probabilistic representation of the underlying network structure for assessing the applicability of different association measures to heavy-tailed degree distributions. Theoretical arguments together with our numerical study indicate that Pearson's coefficient often depends on the size of networks with equal association structure, impeding a systematic comparison of real-world networks. In contrast, Kendall-Gibbons' $\tau_{b}$ is a considerably more robust measure of the degree-degree association

Some results and problems for anisotropic random walks on the plane

This is an expository paper on the asymptotic results concerning path behaviour of the anisotropic random walk on the two-dimensional square lattice Z^2. In recent years Mikl\'os and the authors of the present paper investigated the properties of this random walk concerning strong approximations, local times and range. We give a survey of these results together with some further problems.Comment: 20 page

Relaxation Height in Energy Landscapes: an Application to Multiple Metastable States

The study of systems with multiple (not necessarily degenerate) metastable states presents subtle difficulties from the mathematical point of view related to the variational problem that has to be solved in these cases. We introduce the notion of relaxation height in a general energy landscape and we prove sufficient conditions which are valid even in presence of multiple metastable states. We show how these results can be used to approach the problem of multiple metastable states via the use of the modern theories of metastability. We finally apply these general results to the Blume--Capel model for a particular choice of the parameters ensuring the existence of two multiple, and not degenerate in energy, metastable states

Tunneling and Metastability of continuous time Markov chains

We propose a new definition of metastability of Markov processes on countable state spaces. We obtain sufficient conditions for a sequence of processes to be metastable. In the reversible case these conditions are expressed in terms of the capacity and of the stationary measure of the metastable states

Limiting Behaviour of the Mean Residual Life

In survival or reliability studies, the mean residual life or life expectancy is an important characteristic of the model. Here, we study the limiting behaviour of the mean residual life, and derive an asymptotic expansion which can be used to obtain a good approximation for large values of the time variable. The asymptotic expansion is valid for a quite general class of failure rate distributions--perhaps the largest class that can be expected given that the terms depend only on the failure rate and its derivatives.Comment: 19 page