Perfect and ε-perfect simulation methods for the one-dimensional Kac equation

2016 ◽  
Vol 22 (4) ◽  
Author(s):  
Jem N. Corcoran ◽  
Dale Jennings ◽  
Paul VaughanMiller
Keyword(s):  
Poisson Process ◽  
Single Particle ◽  
Marginal Distribution ◽  
Direct Simulation Monte Carlo ◽  
Equation Model ◽  
Perfect Sampling ◽  
One Dimensional ◽  
Kac Equation ◽  
Simulation Monte Carlo ◽  
The One

AbstractWe review the derivation of the Kac master equation model for random collisions of particles, its relationship to the Poisson process, and existing algorithms for simulating values from the marginal distribution of velocity for a single particle at any given time. We describe and implement a new algorithm that efficiently and more fully leverages properties of the Poisson process, show that it performs at least as well as existing methods, and give empirical evidence that it may perform better at capturing the tails of the single particle velocity distribution. Finally, we derive and implement a novel “ε-perfect sampling” algorithm for the limiting marginal distribution as time goes to infinity. In this case the importance is a proof of concept that has the potential to be expanded to more interesting (DSMC) direct simulation Monte Carlo applications.

On inference in a one-dimensional mosaic and an M/G/∞ queue

1985 ◽  
Vol 17 (01) ◽  
pp. 210-229
Author(s):  
Peter Hall
Keyword(s):  
Poisson Process ◽  
Segment Length ◽  
One Dimensional ◽  
Estimation Procedures ◽  
The One

Suppose segments are distributed at random along a line, their locations being determined by a Poisson process. In the case where segment length is fixed, we compare efficiencies of several different estimates of Poisson intensity. The case of random segment length is also considered, and there we study estimation procedures based on empiric properties. The one-dimensional mosaic may be viewed as an M/G/∞ queue.

scholarly journals Fractional negative binomial and Pólya processes

2018 ◽  
Vol 38 (1) ◽  
pp. 77-101
Author(s):  
Palaniappan Vellai Samy ◽  
Aditya Maheshwari
Keyword(s):  
Poisson Process ◽  
Negative Binomial ◽  
Random Variable ◽  
Infinitely Divisible ◽  
One Dimensional ◽  
Fractional Poisson Process ◽  
Negative Binomial Process ◽  
The One ◽  
Definition Of ◽  
Binomial Process

In this paper, we define a fractional negative binomial process FNBP by replacing the Poisson process by a fractional Poisson process FPP in the gamma subordinated form of the negative binomial process. It is shown that the one-dimensional distributions of the FPP and the FNBP are not infinitely divisible. Also, the space fractional Pólya process SFPP is defined by replacing the rate parameter λ by a gamma random variable in the definition of the space fractional Poisson process. The properties of the FNBP and the SFPP and the connections to PDEs governing the density of the FNBP and the SFPP are also investigated.

EXACT WAVEFUNCTION OF THE ONE-DIMENSIONAL DOUBLE-EXCHANGE MODEL WITH ONE ELECTRON

2012 ◽  
Vol 26 (30) ◽  
pp. 1250154 ◽  
Author(s):  
KYOHEI NAKANO ◽  
ROBERT EDER ◽  
YUKINORI OHTA
Keyword(s):  
Single Particle ◽  
Double Exchange ◽  
Exchange Interactions ◽  
Exchange Model ◽  
Particle Spectrum ◽  
Lower Edge ◽  
One Dimensional ◽  
Mobile Electron ◽  
Spin Excitations ◽  
The One

We study the one-dimensional double-exchange model with L localized spins and one mobile electron. We solve the Schrödinger equation analytically and obtain the energies and wavefunctions for all the eigenstates with spin S = (l-1)/2 exactly. As an application, we compute the single-particle Green's function. We show that, for vanishing exchange interactions between localized spins, the single-particle spectrum is entirely incoherent and the lowest band has an infinite band mass, i.e., the single electron is localized due to its interaction with the spin excitations. For nonvanishing exchange interactions between localized spins, the lower edge of the spectrum acquires a dispersion but the spectrum remains incoherent with no well-defined quasiparticle peak.

On the superposition of m-dimensional point processes

1968 ◽  
Vol 5 (1) ◽  
pp. 169-176 ◽  
Author(s):  
Erhan Çinlar
Keyword(s):  
Poisson Process ◽  
Point Processes ◽  
Natural Extension ◽  
Renewal Processes ◽  
Independent Vector ◽  
One Dimensional ◽  
Independent Components ◽  
Markov Renewal Processes ◽  
The One ◽  
Vector Valued

Consider n independent vector valued point processes. Superposition is defined component by component as a natural extension of the definition for the one-dimensional case. Under proper conditions as n → ∞, it is shown that the superposed process is a many-dimensional Poisson process with independent components. The results are applied to the superposition of Markov renewal processes.

scholarly journals Single-particle excitations and phonon softening in the one-dimensional spinless Holstein model

2005 ◽  
Vol 71 (4) ◽  
Author(s):  
S. Sykora ◽  
A. Hübsch ◽  
K. W. Becker ◽  
G. Wellein ◽  
H. Fehske
Keyword(s):  
Single Particle ◽  
Phonon Softening ◽  
One Dimensional ◽  
Holstein Model ◽  
The One

scholarly journals On the accuracy of bootstrapping sample quantiles of strongly mixing sequences

2007 ◽  
Vol 82 (2) ◽  
pp. 263-282 ◽  
Author(s):  
Shuxia Sun
Keyword(s):  
Rate Of Convergence ◽  
Marginal Distribution ◽  
Regularity Conditions ◽  
One Dimensional ◽  
Strongly Mixing ◽  
Moving Block Bootstrap ◽  
Mixing Sequences ◽  
The One ◽  
Approximations To Distributions ◽  
Sample Quantiles

AbstractIn this paper, we examine the rate of convergence of moving block bootstrap (MBB) approximations to the distributions of normalized sample quantiles based on strongly mixing observations. Under suitable smoothness and regularity conditions on the one-dimensional marginal distribution function, the rate of convergence of the MBB approximations to distributions of centered and scaled sample quantiles is of order O(n−1¼ log logn).

On inference in a one-dimensional mosaic and an M/G/∞ queue

1985 ◽  
Vol 17 (1) ◽  
pp. 210-229 ◽  
Author(s):  
Peter Hall
Keyword(s):  
Poisson Process ◽  
Segment Length ◽  
One Dimensional ◽  
Estimation Procedures ◽  
The One

Suppose segments are distributed at random along a line, their locations being determined by a Poisson process. In the case where segment length is fixed, we compare efficiencies of several different estimates of Poisson intensity. The case of random segment length is also considered, and there we study estimation procedures based on empiric properties. The one-dimensional mosaic may be viewed as an M/G/∞ queue.

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