scholarly journals Scaling limits for the peeling process on random maps

2017 ◽  
Vol 53 (1) ◽  
pp. 322-357 ◽  
Author(s):  
Nicolas Curien ◽  
Jean-François Le Gall
Keyword(s):  
Scaling Limits ◽  
Random Maps ◽  
Peeling Process

scholarly journals The Peeling Process of Infinite Boltzmann Planar Maps

10.37236/5428 ◽  
2016 ◽  
Vol 23 (1) ◽  
Author(s):  
Timothy Budd
Keyword(s):  
Random Walk ◽  
Scaling Limit ◽  
Local Limit ◽  
Critical Weight ◽  
Random Maps ◽  
Simple Interpretation ◽  
Biased Random Walk ◽  
Peeling Process ◽  
General Weight ◽  
Planar Maps

We start by studying a peeling process on finite random planar maps with faces of arbitrary degrees determined by a general weight sequence, which satisfies an admissibility criterion. The corresponding perimeter process is identified as a biased random walk, in terms of which the admissibility criterion has a very simple interpretation. The finite random planar maps under consideration were recently proved to possess a well-defined local limit known as the infinite Boltzmann planar map (IBPM). Inspired by recent work of Curien and Le Gall, we show that the peeling process on the IBPM can be obtained from the peeling process of finite random maps by conditioning the perimeter process to stay positive. The simplicity of the resulting description of the peeling process allows us to obtain the scaling limit of the associated perimeter and volume process for arbitrary regular critical weight sequences.

Random Maps and Their Scaling Limits

2009 ◽  
pp. 197-224 ◽  
Author(s):  
Grégory Miermont
Keyword(s):  
Scaling Limits ◽  
Random Maps

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

CMOS SRAM scaling limits under optimum stability constraints

2013 ◽  
Author(s):  
Adam Makosiej ◽  
Olivier Thomas ◽  
Amara Amara ◽  
Andrei Vladimirescu
Keyword(s):  
Scaling Limits ◽  
Optimum Stability

III-V MOSFETs: Scaling laws, scaling limits, fabrication processes

2010 ◽  
Author(s):  
M. J. W. Rodwell ◽  
B. Shin ◽  
Yong-ju Lee ◽  
S. Steiger ◽  
S. Lee ◽  
...  
Keyword(s):  
Scaling Laws ◽  
Scaling Limits
Sign in / Sign up

Export Citation Format

Share Document