Scaling Limits of Wick Ordered KPZ Equation

2000 ◽  
Vol 209 (3) ◽  
pp. 671-690 ◽  
Author(s):  
Terence Chan
Keyword(s):  
Scaling Limits ◽  
Kpz Equation

scholarly journals Gibbs partitions, Riemann–Liouville fractional operators, Mittag–Leffler functions, and fragmentations derived from stable subordinators

2021 ◽  
Vol 58 (2) ◽  
pp. 314-334
Author(s):  
Man-Wai Ho ◽  
Lancelot F. James ◽  
John W. Lau
Keyword(s):  
Special Functions ◽  
Dirichlet Distribution ◽  
Random Trees ◽  
Fractional Integrals ◽  
Biased Sampling ◽  
Scaling Limits ◽  
Fractional Operators ◽  
Random Partitions ◽  
Two Parameter ◽  
Potential Use

AbstractPitman (2003), and subsequently Gnedin and Pitman (2006), showed that a large class of random partitions of the integers derived from a stable subordinator of index $\alpha\in(0,1)$ have infinite Gibbs (product) structure as a characterizing feature. The most notable case are random partitions derived from the two-parameter Poisson–Dirichlet distribution, $\textrm{PD}(\alpha,\theta)$, whose corresponding $\alpha$-diversity/local time have generalized Mittag–Leffler distributions, denoted by $\textrm{ML}(\alpha,\theta)$. Our aim in this work is to provide indications on the utility of the wider class of Gibbs partitions as it relates to a study of Riemann–Liouville fractional integrals and size-biased sampling, and in decompositions of special functions, and its potential use in the understanding of various constructions of more exotic processes. We provide characterizations of general laws associated with nested families of $\textrm{PD}(\alpha,\theta)$ mass partitions that are constructed from fragmentation operations described in Dong et al. (2014). These operations are known to be related in distribution to various constructions of discrete random trees/graphs in [n], and their scaling limits. A centerpiece of our work is results related to Mittag–Leffler functions, which play a key role in fractional calculus and are otherwise Laplace transforms of the $\textrm{ML}(\alpha,\theta)$ variables. Notably, this leads to an interpretation within the context of $\textrm{PD}(\alpha,\theta)$ laws conditioned on Poisson point process counts over intervals of scaled lengths of the $\alpha$-diversity.

How far will silicon nanocrystals push the scaling limits of NVMs technologies?

2004 ◽  
Author(s):  
B. De Salvo ◽  
C. Gerardi ◽  
S. Lombardo ◽  
T. Baron ◽  
L. Perniola ◽  
...  
Keyword(s):  
Silicon Nanocrystals ◽  
Scaling Limits

RESTRICTED SOLID-ON-SOLID MODEL: FROM LOCAL MORPHOLOGY TO CORRELATION FUNCTIONS AND SCALING EXPONENTS

2004 ◽  
Vol 18 (06) ◽  
pp. 827-840
Author(s):  
CHIH-CHUN CHIEN ◽  
NING-NING PANG ◽  
WEN-JER TZENG
Keyword(s):  
Computer Simulation ◽  
Probability Distribution ◽  
Correlation Functions ◽  
Master Equations ◽  
Interfacial Phenomena ◽  
Solid Model ◽  
Direct Simulation ◽  
Kpz Equation ◽  
Scaling Exponents ◽  
New Approach

We study the restricted solid-on-solid (RSOS) model by grouping consecutive sites into local configurations and obtain the master equations of the probability distribution of these local configurations in closed forms. The obtained solutions to these equations fit very well with those from direct computer simulation of the RSOS model. To demonstrate the effectiveness of this new approach for studying interfacial phenomena, we then calculate the correlation functions and even scaling exponents based on this obtained probability distribution of local configurations. The results are also consistent very well with those obtained from the KPZ equation or direct simulation of the RSOS model.

Densities of scaling limits of coupled continuous time random walks

2016 ◽  
Vol 19 (6) ◽  
Author(s):  
Marcin Magdziarz ◽  
Tomasz Zorawik
Keyword(s):  
Fractional Differential Equations ◽  
Continuous Time ◽  
Stability Index ◽  
Scaling Limits ◽  
Explicit Formulas ◽  
Material Derivative ◽  
Lévy Walks ◽  
Continuous Time Random Walks ◽  
Fractional Differential ◽  
The Stability

AbstractIn this paper we derive explicit formulas for the densities of Lévy walks. Our results cover both jump-first and wait-first scenarios. The obtained densities solve certain fractional differential equations involving fractional material derivative operators. In the particular case, when the stability index is rational, the densities can be represented as an integral of Meijer

Sign in / Sign up

Export Citation Format

Share Document