Abrupt Convergence and Escape Behavior for Birth and Death Chains

We link two phenomena concerning the asymptotical behavior of stochastic processes: (i) abrupt convergence or cut-off phenomenon, and (ii) the escape behavior usually associated to exit from metastability. The former is characterized by convergence at asymptotically deterministic times, while the convergence times for the latter are exponentially distributed. We compare and study both phenomena for discrete-time birth-and-death chains on Z with drift towards zero. In particular, this includes energy-driven evolutions with energy functions in the form of a single well. Under suitable drift hypotheses, we show that there is both an abrupt convergence towards zero and escape behavior in the other direction. Furthermore, as the evolutions are reversible, the law of the final escape trajectory coincides with the time reverse of the law of cut-off paths. Thus, for evolutions defined by one-dimensional energy wells with sufficiently steep walls, cut-off and escape behavior are related by time inversion.Comment: 2 figure

Phase Transition in Ferromagnetic Ising Models with Non-Uniform External Magnetic Fields

In this article we study the phase transition phenomenon for the Ising model under the action of a non-uniform external magnetic field. We show that the Ising model on the hypercubic lattice with a summable magnetic field has a first-order phase transition and, for any positive (resp. negative) and bounded magnetic field, the model does not present the phase transition phenomenon whenever $\liminf h_i> 0$, where ${\bf h} = (h_i)_{i \in \Z^d}$ is the external magnetic field.Comment: 11 pages. Published in Journal of Statistical Physics - 201

Metastability and Nucleation for the Blume-Capel Model. Different mechanisms of transition

We study metastability and nucleation for the Blume-Capel model: a ferromagnetic nearest neighbour two-dimensional lattice system with spin variables taking values in -1,0,+1. We consider large but finite volume, small fixed magnetic field h and chemical potential "lambda" in the limit of zero temperature; we analyze the first excursion from the metastable -1 configuration to the stable +1 configuration. We compute the asymptotic behaviour of the transition time and describe the typical tube of trajectories during the transition. We show that, unexpectedly, the mechanism of transition changes abruptly when the line h=2*lambda is crossed.Comment: 96 pages, 44 tex-figures, 7 postscript figure

Critical droplets in Metastable States of Probabilistic Cellular Automata

We consider the problem of metastability in a probabilistic cellular automaton (PCA) with a parallel updating rule which is reversible with respect to a Gibbs measure. The dynamical rules contain two parameters $\beta$ and $h$ which resemble, but are not identical to, the inverse temperature and external magnetic field in a ferromagnetic Ising model; in particular, the phase diagram of the system has two stable phases when $\beta$ is large enough and $h$ is zero, and a unique phase when $h$ is nonzero. When the system evolves, at small positive values of $h$, from an initial state with all spins down, the PCA dynamics give rise to a transition from a metastable to a stable phase when a droplet of the favored $+$ phase inside the metastable $-$ phase reaches a critical size. We give heuristic arguments to estimate the critical size in the limit of zero ``temperature'' ($\beta\to\infty$), as well as estimates of the time required for the formation of such a droplet in a finite system. Monte Carlo simulations give results in good agreement with the theoretical predictions.Comment: 5 LaTeX picture

Proceedings of the third French-Ukrainian workshop on the instrumentation developments for HEP

The reports collected in these proceedings have been presented in the third French-Ukrainian workshop on the instrumentation developments for high-energy physics held at LAL, Orsay on October 15-16. The workshop was conducted in the scope of the IDEATE International Associated Laboratory (LIA). Joint developments between French and Ukrainian laboratories and universities as well as new proposals have been discussed. The main topics of the papers presented in the Proceedings are developments for accelerator and beam monitoring, detector developments, joint developments for large-scale high-energy and astroparticle physics projects, medical applications.Comment: 3rd French-Ukrainian workshop on the instrumentation developments for High Energy Physics, October 15-16, 2015, LAL, Orsay, France, 94 page

Large Deviations Analysis for Distributed Algorithms in an Ergodic Markovian Environment

We provide a large deviations analysis of deadlock phenomena occurring in distributed systems sharing common resources. In our model transition probabilities of resource allocation and deallocation are time and space dependent. The process is driven by an ergodic Markov chain and is reflected on the boundary of the d-dimensional cube. In the large resource limit, we prove Freidlin-Wentzell estimates, we study the asymptotic of the deadlock time and we show that the quasi-potential is a viscosity solution of a Hamilton-Jacobi equation with a Neumann boundary condition. We give a complete analysis of the colliding 2-stacks problem and show an example where the system has a stable attractor which is a limit cycle

Random-cluster representation of the Blume-Capel model

The so-called diluted-random-cluster model may be viewed as a random-cluster representation of the Blume--Capel model. It has three parameters, a vertex parameter $a$, an edge parameter $p$, and a cluster weighting factor $q$. Stochastic comparisons of measures are developed for the `vertex marginal' when $q\in[1,2]$, and the `edge marginal' when q\in[1,\oo). Taken in conjunction with arguments used earlier for the random-cluster model, these permit a rigorous study of part of the phase diagram of the Blume--Capel model

A New Limit on the Neutrinoless DBD of 130Te

We report the present results of CUORICINO a cryogenic experiment on neutrinoless double beta decay (DBD) of 130Te consisting of an array of 62 crystals of TeO2 with a total active mass of 40.7 kg. The array is framed inside of a dilution refrigerator, heavily shielded against environmental radioactivity and high-energy neutrons, and operated at a temperature of ~8 mK in the Gran Sasso Underground Laboratory. Temperature pulses induced by particle interacting in the crystals are recorded and measured by means of Neutron Transmutation Doped thermistors. The gain of each bolometer is stabilized with voltage pulses developed by a high stability pulse generator across heater resistors put in thermal contact with the absorber. The calibration is performed by means of two thoriated wires routinely inserted in the set-up. No evidence for a peak indicating neutrinoless DBD of 130Te is detected and a 90% C.L. lower limit of 1.8E24 years is set for the lifetime of this process. Taking largely into account the uncertainties in the theoretical values of nuclear matrix elements, this implies an upper boud on the effective mass of the electron neutrino ranging from 0.2 to 1.1 eV. This sensitivity is similar to those of the 76Ge experiments.Comment: 4 pages, 2 figure

Uniparental Genetic Heritage of Belarusians: Encounter of Rare Middle Eastern Matrilineages with a Central European Mitochondrial DNA Pool

Ethnic Belarusians make up more than 80% of the nine and half million people inhabiting the Republic of Belarus. Belarusians together with Ukrainians and Russians represent the East Slavic linguistic group, largest both in numbers and territory, inhabiting East Europe alongside Baltic-, Finno-Permic- and Turkic-speaking people. Till date, only a limited number of low resolution genetic studies have been performed on this population. Therefore, with the phylogeographic analysis of 565 Y-chromosomes and 267 mitochondrial DNAs from six well covered geographic sub-regions of Belarus we strove to complement the existing genetic profile of eastern Europeans. Our results reveal that around 80% of the paternal Belarusian gene pool is composed of R1a, I2a and N1c Y-chromosome haplogroups – a profile which is very similar to the two other eastern European populations – Ukrainians and Russians. The maternal Belarusian gene pool encompasses a full range of West Eurasian haplogroups and agrees well with the genetic structure of central-east European populations. Our data attest that latitudinal gradients characterize the variation of the uniparentally transmitted gene pools of modern Belarusians. In particular, the Y-chromosome reflects movements of people in central-east Europe, starting probably as early as the beginning of the Holocene. Furthermore, the matrilineal legacy of Belarusians retains two rare mitochondrial DNA haplogroups, N1a3 and N3, whose phylogeographies were explored in detail after de novo sequencing of 20 and 13 complete mitogenomes, respectively, from all over Eurasia. Our phylogeographic analyses reveal that two mitochondrial DNA lineages, N3 and N1a3, both of Middle Eastern origin, might mark distinct events of matrilineal gene flow to Europe: during the mid-Holocene period and around the Pleistocene-Holocene transition, respectively