Percolation for the stable marriage of Poisson and Lebesgue

Let $\Xi$ be the set of points (we call the elements of $\Xi$ centers) of Poisson process in $\R^d$, $d\geq 2$, with unit intensity. Consider the allocation of $\R^d$ to $\Xi$ which is stable in the sense of Gale-Shapley marriage problem and in which each center claims a region of volume $\alpha\leq 1$. We prove that there is no percolation in the set of claimed sites if $\alpha$ is small enough, and that, for high dimensions, there is percolation in the set of claimed sites if $\alpha<1$ is large enough.Comment: revised version (only minor correction since v2), 16 pages, 3 figure

Low temperature microwave emission from molecular clusters

We investigate the experimental detection of the electromagnetic radiation generated in the fast magnetization reversal in Mn12-acetate at low temperatures. In our experiments we used large single crystals and assemblies of several small single crystals of Mn12-acetate placed inside a cylindrical stainless steel waveguide in which an InSb hot electron device was also placed to detect the radiation. All this was set inside a SQUID magnetometer that allowed to change the magnetic field and measure the magnetic moment and the temperature of the sample as the InSb detected simultaneously the radiation emitted from the molecular magnets. Our data show a sequential process in which the fast inversion of the magnetic moment first occurs, then the radiation is detected by the InSb device, and finally the temperature of the sample increases during 15 ms to subsequently recover its original value in several hundreds of milliseconds.Comment: changed conten

A local limit theorem for triple connections in subcritical Bernoulli percolation

We prove a local limit theorem for the probability of a site to be connected by disjoint paths to three points in subcritical Bernoulli percolation on $\mathbb{Z}^{d},\,d\geq2$ in the limit where their distances tend to infinity.Comment: 31 page

Angular asymptotics for multi-dimensional non-homogeneous random walks with asymptotically zero drift

We study the first exit time $\tau$ from an arbitrary cone with apex at the origin by a non-homogeneous random walk (Markov chain) on $\Z^d$ ($d \geq 2$) with mean drift that is asymptotically zero. Specifically, if the mean drift at \bx \in \Z^d is of magnitude O(\| \bx\|^{-1}), we show that $\tau<\infty$ a.s. for any cone. On the other hand, for an appropriate drift field with mean drifts of magnitude \| \bx\|^{-\beta}, $\beta \in (0,1)$, we prove that our random walk has a limiting (random) direction and so eventually remains in an arbitrarily narrow cone. The conditions imposed on the random walk are minimal: we assume only a uniform bound on $2$nd moments for the increments and a form of weak isotropy. We give several illustrative examples, including a random walk in random environment model

Bulk-sensitive Photoemission of Mn5Si3

We have carried out a bulk-sensitive high-resolution photoemission experiment on Mn5Si3. The measurements are performed for both core level and valence band states. The Mn core level spectra are deconvoluted into two components corresponding to different crystallographic sites. The asymmetry of each component is of noticeable magnitude. In contrast, the Si 2p spectrum shows a simple Lorentzian shape with low asymmetry. The peaks of the valence band spectrum correspond well to the peak positions predicted by the former band calculation.Comment: To be published in: Solid State Communication

Russian Lexicographic Landscape: a Tale of 12 Dictionaries

The paper reports on quantitative analysis of 12 Russian dictionaries at three levels: 1) headwords: The size and overlap of word lists, coverage of large corpora, and presence of neologisms; 2) synonyms: Overlap of synsets in different dictionaries; 3) definitions: Distribution of definition lengths and numbers of senses, as well as textual similarity of same-headword definitions in different dictionaries. The total amount of data in the study is 805,900 dictionary entries, 892,900 definitions, and 84,500 synsets. The study reveals multiple connections and mutual influences between dictionaries, uncovers differences in modern electronic vs. traditional printed resources, as well as suggests directions for development of new and improvement of existing lexical semantic resources

Non-homogeneous random walks with non-integrable increments and heavy-tailed random walks on strips

We study asymptotic properties of spatially non-homogeneous random walks with non-integrable increments, including transience, almost-sure bounds, and existence and non existence of moments for first-passage and last-exit times. In our proofs we also make use of estimates for hitting probabilities and large deviations bounds. Our results are more general than existing results in the literature, which consider only the case of sums of independent (typically, identically distributed) random variables. We do not assume the Markov property. Existing results that we generalize include a circle of ideas related to the Marcinkiewicz-Zygmund strong law of large numbers, as well as more recent work of Kesten and Maller. Our proofs are robust and use martingale methods. We demonstrate the benefit of the generality of our results by applications to some non-classical models, including random walks with heavy-tailed increments on two-dimensional strips, which include, for instance, certain generalized risk processes