1,857 research outputs found
Lattice permutations and Poisson-Dirichlet distribution of cycle lengths
No full textWe study random spatial permutations on ℤ3 where each jump x↦π(x) is penalized by a factor e−T∥x−π(x)∥2 . The system is known to exhibit a phase transition for low enough T where macroscopic cycles appear. We observe that the lengths of such cycles are distributed according to Poisson-Dirichlet. This can be explained heuristically using a stochastic coagulation-fragmentation process for long cycles, which is supported by numerical data
Self-alignment driven by jump processes: Macroscopic limit and numerical investigation
No full textIn this paper, we are interested in studying self-alignment mechanisms described as jump processes. In the dynamics proposed, active particles are moving at a constant speed and align with their neighbors at random times following a Poisson process. This dynamics can be viewed as an asynchronous version of the so-called Vicsek model. Starting from this particle dynamics, we introduce the related kinetic description and then derive a continuum hydrodynamic model. We then introduce different discretization strategies for the hierarchy of proposed models, we numerically study the convergence of the schemes and compare the behaviors of the different systems for several test cases
Normal deviation and Poisson approximation of a security market by the geometric Markov renewal processes
No full textWe consider the geometric Markov renewal processes (GMRP) as a model for a security market. Normal deviations of the geometric Markov renewal processes for ergodic averaging and double averaging schemes are derived. We introduce Poisson averaging scheme for the geometric Markov renewal processes. European call option pricing formulas for GMRP are presented. [ABSTRACT FROM AUTHOR
Bending Poisson Effect in Two-Dimensional Crystals
No full textAs the Poisson effect formulates, lateral strains in a material can be caused by a uniaxial stress in the perpendicular direction, but no net lateral strain should be induced in a thin homogeneous elastic plate subjected to a pure bending load. Here, we demonstrated by ab initio simulations that significant exotic lateral strains can be induced by pure bending in two-dimensional crystals, in which the lateral components of chemical bonds can respond to bending curvature directly. The bending Poisson ratio, defined as the ratio of lateral strain to the curvature, is a function of curvature depending on chemical constitution, bonding structure, and atomic interaction of the crystal, and is anisotropic
Poisson Indices of Segregation
No full textExisting indices of residential segregation are based on an arbitrary partition of the city in neighborhoods: given a spatial distribution of racial groups, the index provides different levels of segregation for different partitions. This paper proposes a method in which individual locations are mapped to aggregate levels of segregation, avoiding arbitrary partitions. Assuming a simple spatial process driving the locations of different racial groups, I define a location-specific segregation index and measure the city-level segregation as average of the individual index. After deriving several distributional results for this family of indices, I apply the idea to US Census data, using nonparametric estimation techniques. This approach provides different levels and rankings of cities' segregation than traditional indices. I show that high aggregate levels of spatial separation are the result of very few locations with extremely high local segregation. I replicate the study of Cutler and Glaeser (1997) showing that their results change when segregation is measured using my approach. These findings potentially challenge the robustness of previous studies about the impact of segregation on socioeconomic outcomes.spatial segregation, spatial processes, nonparametric estimation
Accurate representation of the distributions of the 3D Poisson-Voronoi typical cell geometrical features
No full textUnderstanding the intricate and complex materials microstructure and how it is related to materials properties is an important problem in the Materials Science field. For a full comprehension of this relation, it is fundamental to be able to describe the main characteristics of the 3-dimensional microstructure. The most basic model used for approximating steel microstructure is the Poisson-Voronoi diagram. Poisson-Voronoi diagrams have interesting mathematical properties, and they are used as a good model for single-phase materials. In this paper we exploit the scaling property of the underlying Poisson process to derive the distribution of the main geometrical features of the grains for every value of the intensity parameter. Moreover, we use a sophisticated simulation program to construct a close Monte Carlo based approximation for the distributions of interest. Using this, we determine the closest approximating distributions within the mentioned frequently used parametric classes of distributions and conclude that these representations can be quite accurate. Finally we consider a 3D volume dataset and compare the real volume distribution to what is to be expected under the Poisson-Voronoi model.Accepted author manuscriptStatisticsMaterials Science and Engineering(OLD) MSE-
A Multivariate Poisson Model with Exible Dependence Structure
No full textMultivariate distributions are indispensable tools for modeling complex data structures with multiple dependent variables. Despite extensive research on discrete multivariate distributions, the multivariate Poisson distribution remains inadequately defined. However, multivariate Poisson counts are not rare and have gained considerable attention in scientific fields such as reliability engineering. Accurately specifying the dependence structure presents a significant challenge in analyzing such data. Although several methods have been proposed in the literature to address this issue, they have limitations in satisfying all feasible correlations. Currently, there is an outstanding question regarding the development of a multivariate Poisson model that is easily interpretable and effectively handles dependent Poisson counts.In this study, we present a novel multivariate Poisson model that leverages multivariate reduction techniques (MRT) to enable greater flexibility in the dependence structure, particularly for negative correlations, than classical constructions. Our proposed model generalizes existing MRT-based methods by having the same parameters when some of our model's parameters are preset. We demonstrate the feasible regions of correlations and show that our model overcomes the limitations of previous methods, making it ideal for analyzing multivariate Poisson counts. Furthermore, we establish several probabilistic properties, including the probability mass function, the probability-generating function, and the Pearson correlation coefficient. We also provide a detailed discussion of maximum likelihood estimation and an algorithm for generating multivariate Poisson random variables. Our model's superiority is demonstrated through simulations and a real-world example.Statistic
Thermodynamical versus log-Poisson distribution in turbulence
No full textThe thermodynamical model of intermittency in fully developed turbulence due to Castaing (B. Castaing, J. Phys. II France 6 (1996) 105) is investigated and compared with the log-Poisson model (Z-S, She, E. Leveque, Phys. Rev. Lett. 72 (1994) 336). It is shown that the thermodynamical model obeys general scaling laws and corresponds to the degenerate class of scale-invariant statistics. We also find that its structure function shapes have physical behaviors similar to the log-Poisson's one. The only difference between them lies in the convergence of the log-Poisson's structure functions and divergence of the thermodynamical one. As far as the comparison with experiments on intermittency is concerned, they are indifferent
The Poisson Process
No full textCreated by Kyle Siegrist of the University of Alabama-Huntsville, this online, interactive lesson on the Poisson process provides examples, exercises, and applets. Specific topics include the exponential distribution, gamma distribution, Poisson distribution, splitting a Poisson process, analogy with Bernoulli trials, and higher dimensional Poisson processes. Additionally, the author offers external resources for those interested in further study of this statistical concept. Overall, this is a nice resource as it provides students with definitions and then allows them to apply these theories in the form of interactive applets
A characterization of the Poisson distribution
No full textIn 1976 the author of this note provided a characterization of the Poisson distribution in the set of infinitely divisible distributions. We give another characterization of the Poisson distribution in the set of infinitely divisible distributions.Poisson distribution Infinitely divisible distributions
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