Lyapunov exponents of Green's functions for random potentials tending to zero

We consider quenched and annealed Lyapunov exponents for the Green's function of $-\Delta+\gamma V$, where the potentials $V(x), x\in\Z^d$, are i.i.d. nonnegative random variables and $\gamma>0$ is a scalar. We present a probabilistic proof that both Lyapunov exponents scale like $c\sqrt{\gamma}$ as $\gamma$ tends to 0. Here the constant $c$ is the same for the quenched as for the annealed exponent and is computed explicitly. This improves results obtained previously by Wei-Min Wang. We also consider other ways to send the potential to zero than multiplying it by a small number.Comment: 16 pages, 3 figures. 1 figure added, very minor corrections. To appear in Probability Theory and Related Fields. The final publication is available at http://www.springerlink.com, see http://www.springerlink.com/content/p0873kv68315847x/?p=4106c52fc57743eba322052bb931e8ac&pi=21

Quenched large deviations for multidimensional random walk in random environment with holding times

We consider a random walk in random environment with random holding times, that is, the random walk jumping to one of its nearest neighbors with some transition probability after a random holding time. Both the transition probabilities and the laws of the holding times are randomly distributed over the integer lattice. Our main result is a quenched large deviation principle for the position of the random walk. The rate function is given by the Legendre transform of the so-called Lyapunov exponents for the Laplace transform of the first passage time. By using this representation, we derive some asymptotics of the rate function in some special cases.Comment: This is the corrected version of the paper. 24 page

Molecular Spiders with Memory

Synthetic bio-molecular spiders with "legs" made of single-stranded segments of DNA can move on a surface which is also covered by single-stranded segments of DNA complementary to the leg DNA. In experimental realizations, when a leg detaches from a segment of the surface for the first time it alters that segment, and legs subsequently bound to these altered segments more weakly. Inspired by these experiments we investigate spiders moving along a one-dimensional substrate, whose legs leave newly visited sites at a slower rate than revisited sites. For a random walk (one-leg spider) the slowdown does not effect the long time behavior. For a bipedal spider, however, the slowdown generates an effective bias towards unvisited sites, and the spider behaves similarly to the excited walk. Surprisingly, the slowing down of the spider at new sites increases the diffusion coefficient and accelerates the growth of the number of visited sites.Comment: 10 pages, 3 figure

Positive temperature versions of two theorems on first-passage percolation

The estimates on the fluctuations of first-passsage percolation due to Talagrand (a tail bound) and Benjamini--Kalai--Schramm (a sublinear variance bound) are transcribed into the positive-temperature setting of random Schroedinger operators.Comment: 15 pp; to appear in GAFA Seminar Note

Laplacian Growth, Elliptic Growth, and Singularities of the Schwarz Potential

The Schwarz function has played an elegant role in understanding and in generating new examples of exact solutions to the Laplacian growth (or "Hele- Shaw") problem in the plane. The guiding principle in this connection is the fact that "non-physical" singularities in the "oil domain" of the Schwarz function are stationary, and the "physical" singularities obey simple dynamics. We give an elementary proof that the same holds in any number of dimensions for the Schwarz potential, introduced by D. Khavinson and H. S. Shapiro [17] (1989). A generalization is also given for the so-called "elliptic growth" problem by defining a generalized Schwarz potential. New exact solutions are constructed, and we solve inverse problems of describing the driving singularities of a given flow. We demonstrate, by example, how \mathbb{C}^n - techniques can be used to locate the singularity set of the Schwarz potential. One of our methods is to prolong available local extension theorems by constructing "globalizing families". We make three conjectures in potential theory relating to our investigation

Equality of averaged and quenched large deviations for random walks in random environments in dimensions four and higher

We consider large deviations for nearest-neighbor random walk in a uniformly elliptic i.i.d. environment. It is easy to see that the quenched and the averaged rate functions are not identically equal. When the dimension is at least four and Sznitman's transience condition (T) is satisfied, we prove that these rate functions are finite and equal on a closed set whose interior contains every nonzero velocity at which the rate functions vanish.Comment: 17 pages. Minor revision. In particular, note the change in the title of the paper. To appear in Probability Theory and Related Fields

Insight into the mechanism of modulated syntheses: in situ synchrotron diffraction studies on the formation of Zr-fumarate MOF

In this work, the formation of a Zr-based metal-organic framework (MOF), Zr-fumarate MOF (Zr-fum MOF), is studied in situ by energy-dispersive diffraction. The Zr-fum MOF can be synthesised in DMF as well as in water-based synthesis systems. In both cases, its formation requires modulation, i.e. a monocarboxylic acid which is used as the modulator has to be added to the synthesis mixture. In general, different mechanisms of modulation are possible, for example, deprotonation of the linker molecule (deprotonation modulation) or coordination modulation (wherein the molecules of the modulator compete with the linker molecules for the coordination sites at the inorganic building units). Independently of the specific mechanism, modulation often improves the reproducibility of the MOF synthesis and the crystallinity of the product and may be used to control crystal size and morphology. This study is the first to investigate the kinetics of modulated MOF syntheses with regard to coordination modulation. According to this concept, the addition of a modulator usually decelerates the reaction. Our kinetic investigations show that this is the case for the formation of Zr-fum MOF in the water-based synthesis with formic acid used as a modulator. On the contrary, the addition of formic acid to the DMF-based synthesis results in an accelerating effect. This unexpected effect can be attributed to a small amount of water present in formic acid. Correspondingly, the addition of water to the synthesis mixture also showed an accelerating effect. These investigations emphasise the subtle interplay of the different ingredients in a MOF synthesis. In the case of the Zr-fum MOF, both the modulator formic acid and the water content strongly affect the kinetics of crystallisation. Quantitative evaluation of the kinetic data using the Gualtieri equation provides additional insight into the mechanisms of coordination-modulated MOF formation reactions and excludes the idea of deprotonation modulation.DFG/Porous Metal–Organic Frameworks/1362DESY/I-2011055

Starting the conversation: land issues and critical conservation studies in post-colonial Africa

This thematic issue brings together the scholarly fields of critical conservation studies and African land issues, a relationship largely unexplored to date. The alienation of land for conservation purposes, introduced to Africa under colonial rule and still taking place today, has fundamental impacts on the politics of land and land use, and is contested in contemporary nation-states - including those that are attempting to implement land restitution and reform. The contributors explore these issues in a range of African contexts. Three key themes are identified: the problematic constructions of ‘community’ by outside agencies; spatial exclusion and the silencing of local voices; and the neoliberalisation of conservation spaces. In contributing to new perspectives on these themes, this thematic issue shows how discourses and practices of conservation, increasingly shaped by neoliberalism, currently impact on land ownership, access and use. It further highlights some important historical continuities. These trends can be observed in transfrontier conservation areas, on state-owned land used for conservation and ‘green’ initiatives, but also on private land where conservation is increasingly turned to commercial purposes.International Bibliography of Social Science

Excited Random Walk in One Dimension

We study the excited random walk, in which a walk that is at a site that contains cookies eats one cookie and then hops to the right with probability p and to the left with probability q=1-p. If the walk hops onto an empty site, there is no bias. For the 1-excited walk on the half-line (one cookie initially at each site), the probability of first returning to the starting point at time t scales as t^{-(2-p)}. Although the average return time to the origin is infinite for all p, the walk eats, on average, only a finite number of cookies until this first return when p<1/2. For the infinite line, the probability distribution for the 1-excited walk has an unusual anomaly at the origin. The positions of the leftmost and rightmost uneaten cookies can be accurately estimated by probabilistic arguments and their corresponding distributions have power-law singularities near the origin. The 2-excited walk on the infinite line exhibits peculiar features in the regime p>3/4, where the walk is transient, including a mean displacement that grows as t^{nu}, with nu>1/2 dependent on p, and a breakdown of scaling for the probability distribution of the walk.Comment: 14 pages, 13 figures, 2-column revtex4 format, for submission to J. Phys.