912 research outputs found
Percolation for the stable marriage of Poisson and Lebesgue
Let be the set of points (we call the elements of centers) of
Poisson process in , , with unit intensity. Consider the
allocation of to which is stable in the sense of Gale-Shapley
marriage problem and in which each center claims a region of volume . We prove that there is no percolation in the set of claimed sites if
is small enough, and that, for high dimensions, there is percolation
in the set of claimed sites if 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
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 from an arbitrary cone with apex at the origin by a non-homogeneous random walk (Markov chain) on () 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 a.s. for any cone. On the other hand, for an appropriate drift field with mean drifts of magnitude \| \bx\|^{-\beta}, , 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 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
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