arXiv subjects

Zhipeng Liu

Publications and source records attributed to Zhipeng Liu.

66 records · Page 4Linked to original sources

arXiv2017

Malliavin-based Multilevel Monte Carlo Estimators for Densities of Max-stable Processes

We introduce a class of unbiased Monte Carlo estimators for the multivariate density of max-stable fields generated by Gaussian processes. Our estimators take advantage of recent results on exact simulation of max-stable fields combined with identities studied in the Malliavin calculus literature and ideas developed in the multilevel Monte Carlo literature. Our approach allows estimating multivariate densities of max-stable fields with precision $\varepsilon $ at a computational cost of order $O\left( \varepsilon ^{-2}\log \log \log \left( 1/\varepsilon \right) \right) $.

stat.CO↗

arXiv2016

Exact Sampling of the Infinite Horizon Maximum of a Random Walk Over a Non-linear Boundary

We present the first algorithm that samples $\max_{n\geq0}\{S_{n}-n^α\},$ where $S_n$ is a mean zero random walk, and $n^α$ with $α\in(1/2,1)$ defines a nonliner boundary. We show that our algorithm has finite expected running time. We also apply the algorithm to construct the first exact simulation method for the steady-state departure process of a $GI/GI/\infty$ queue where the service time distribution has infinite mean.

math.PR↗

arXiv2016

TASEP on a ring in sub-relaxation time scale

Interacting particle systems in the KPZ universality class on a ring of size $L$ with $O(L)$ number of particles are expected to change from KPZ dynamics to equilibrium dynamics at the so-called relaxation time scale $t=O(L^{3/2})$. In particular the system size is expected to have little effect to the particle fluctuations in the sub-relaxation time scale $t\ll L^{3/2}$. We prove that this is indeed the case for the totally asymmetric simple exclusion process (TASEP) with two types of initial conditions. For flat initial condition, we show that the particle fluctuations are given by the Airy$_1$ process as in the infinite TASEP with flat initial condition. On the other hand, the TASEP on a ring with step initial condition is equivalent to the periodic TASEP with a certain shock initial condition. We compute the fluctuations explicitly both away from and near the shocks for the infinite TASEP with same initial condition, and then show that the periodic TASEP has same fluctuations in the sub-relaxation time scale.

math.PR↗

arXiv2015

Fluctuations of TASEP and LPP with general initial data

We prove Airy process variational formulas for the one-point probability distribution of (discrete time parallel update) TASEP with general initial data, as well as last passage percolation from a general lattice path to a point. We also consider variants of last passage percolation with inhomogeneous parameter geometric weights and provide variational formulas of a similar nature. This proves one aspect of the conjectural description of the renormalization fixed point of the Kardar-Parisi-Zhang universality class.

math.PR↗

arXiv2013

On the average of the Airy process and its time reversal

We show that the supremum of the average of the Airy process and its time reversal minus a parabola is distributed as the maximum of two independent GUE Tracy-Widom random variables. The proof is obtained by considering a directed last passage percolation model with a rotational symmetry in two different ways. We also review other known identities between the Airy process and the Tracy-Widom distributions.

math.PR↗

arXiv2013

Discrete Toeplitz/Hankel determinants and the width of non-intersecting processes

We show that the ratio of a discrete Toeplitz/Hankel determinant and its continuous counterpart equals a Freholm determinant involving continuous orthogonal polynomials. This identity is used to evaluate a triple asymptotic of some discrete Toeplitz/Hankel determinants which arise in studying non-intersecting processes. We show that the asymptotic fluctuations of the width of such processes are given by the GUE Tracy-Widom distribution. This result leads us to an identity between the GUE Tracy-Widom distribution and the maximum of the sum of two independent Airy processes minus a parabola. We provide an independent proof of this identity.

math.PR↗

arXiv2012

Dust-acoustic waves and stability in the permeating dusty plasma: I. Maxwellian distribution

The dust-acoustic waves and their stability in the permeating dusty plasma with the Maxwellian velocity distribution are investigated. We derive the dust-acoustic wave frequency and instability growth rate in two limiting physical cases that the thermal velocity of the flowing dusty plasma is (a) much larger than, and (b) much smaller than the phase velocity of the waves. We find that the stability of the waves depend strongly on the velocity of the flowing dusty plasma in the permeating dusty plasma. The numerical analyses are made based on the example that a cometary plasma tail is passing through the interplanetary space plasma. We show that, in case (a), the waves are generally unstable for any flowing velocity, but in case (b), the waves become unstable only when the wave number is small and the flowing velocity is large. When the physical conditions are between these two limiting cases, we gain a strong insight into the dependence of the stability criterions on the physical conditions in the permeating dusty plasma.

physics.plasm-ph↗

arXiv2012

Dust-acoustic waves and stability in the permeating dusty plasma: II. Power-law distributions

The dust-acoustic waves and their stability driven by a flowing dusty plasma when it cross through a static (target) dusty plasma (the so-called permeating dusty plasma) are investigated when the components of the dusty plasma obey the power-law q-distributions in nonextensive statistics. The frequency, the growth rate and the stability condition of the dust-acoustic waves are derived under this physical situation, which express the effects of the nonextensivity as well as the flowing dusty plasma velocity on the dust-acoustic waves in this dusty plasma. The numerical results illustrate some new characteristics of the dust-acoustic waves, which are different from those in the permeating dusty plasma when the plasma components are the Maxwellian distribution. In addition, we show that the flowing dusty plasma velocity has a significant effect on the dust-acoustic waves in the permeating dusty plasma with the power-law q-distribution.

physics.plasm-ph↗

arXiv2009

Dust-acoustic instability driven by drifting ions and electrons in the dust plasma with Lorentzian kappa distribution

The instability of the dust-acoustic waves driven by drifting electrons and ions in a dusty plasma is investigated by the kinetic theory. All the plasma components (electrons, ions and dust particles) are assumed to be the Lorentzian kappa-distributions. The spectral indexes kappa of the kappa-distributions for the three plasma components are different from each other. The obtained instability growth rate depends on the physical quantities of the plasma not only, but on the spectral indexes. The numerical results for the kappa-effect on the instability growth rate show that, if the normalized wave number is small, the index of electrons has a stabilized effect on the dust acoustic waves and the index of ions has an instability effect on the waves, but if the normalized wave number is large, they both nearly have no any effect on the waves. In reverse, the index of dust grains has nearly no any effect on the instability growth rate if the normalized wave number is small, but it has a stabilized effect on the dust waves if the normalized wave number is large.

physics.plasm-ph↗

arXiv2009

A nonextensive approach for the instability of current-driven ion-acoustic waves in space plasma

The instability of current-driven ion-acoustic waves in the collisionless magnetic-field-free space plasma is investigated by using a nonextensive approach. The ions and the electrons are thought of in the power-law distributions that can be described by the generalized q-Maxwellian velocity distribution and are considered with the different nonextensive q-parameters. The generalized q-wave frequency and the generalized instability q-growth rate for the ion-acoustic waves are derived. The numerical results show that the nonextensive effects on the ion-acoustic waves are not apparent when the electron temperature is much more than the ion temperature, but they are salient when the electron temperature is not much more than the ion temperature. As compared with the electrons, the ions play a dominant role in the nonextensive effects.

physics.plasm-ph↗

arXiv2008

Stability analysis of the classical ideal gas in nonextensive statistics and the negative specific heat

We present a stability analysis of the classical ideal gas in a new theory of nonextensive statistics and use the theory to understand the phenomena of negative specific heat in some self-gravitating systems. The stability analysis is made on the basis of the second variation of Tsallis entropy. It is shown that the system is thermodynamically unstable if the nonextensive parameter is q>5/3, which is exactly equivalent to the condition of appearance of the negative specific heat.

cond-mat.stat-mech↗

arXiv2008

Nonextensivity and q-distribution of a relativistic gas under an external electromagnetic field

We investigate the nonextensivity and the q-distribution of a relativistic gas under an external electromagnetic field. We derive a formula expression of the nonextensive parameter q based on the relativistic generalized Boltzmann equation, the relativistic q-H theorem and the relativistic version of q-power-law distribution function in the nonextensive q-kinetic theory. We thus provide the connection between the parameter 1-q and the differentiation of the temperature field of the gas as well as the four-potential with respect to time and space coordinates, and therefore present the nonextensivity for the gas a clearly physical meaning.

cond-mat.stat-mech↗