scholarly journals Scaling limits for the critical Fortuin-Kasteleyn model on a random planar map II: local estimates and empty reduced word exponent

2017 ◽  
Vol 22 (0) ◽  
Author(s):  
Ewain Gwynne ◽  
Xin Sun
Keyword(s):  
Scaling Limits ◽  
Planar Map ◽  
Reduced Word ◽  
Random Planar Map

scholarly journals Scaling limits for the critical Fortuin–Kasteleyn model on a random planar map I: Cone times

2019 ◽  
Vol 55 (1) ◽  
pp. 1-60 ◽  
Author(s):  
Ewain Gwynne ◽  
Cheng Mao ◽  
Xin Sun
Keyword(s):  
Scaling Limits ◽  
Planar Map ◽  
Random Planar Map

scholarly journals External diffusion-limited aggregation on a spanning-tree-weighted random planar map

2021 ◽  
Vol 49 (4) ◽  
Author(s):  
Ewain Gwynne ◽  
Joshua Pfeffer
Keyword(s):  
Spanning Tree ◽  
Diffusion Limited Aggregation ◽  
Planar Map ◽  
External Diffusion ◽  
Diffusion Limited ◽  
Random Planar Map

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

scholarly journals Liouville first-passage percolation: Subsequential scaling limits at high temperature

2019 ◽  
Vol 47 (2) ◽  
pp. 690-742 ◽  
Author(s):  
Jian Ding ◽  
Alexander Dunlap
Keyword(s):  
High Temperature ◽  
Scaling Limits ◽  
First Passage Percolation ◽  
First Passage

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

Scaling limits of interacting diffusions with arbitrary initial distributions

1994 ◽  
Vol 99 (1) ◽  
pp. 97-110 ◽  
Author(s):  
K�hei Uchiyama
Keyword(s):  
Scaling Limits ◽  
Interacting Diffusions ◽  
Initial Distributions

Double scaling limits, Airy functions and multicritical behaviour in O(N) vector sigma models

1996 ◽  
Vol 49 (1-3) ◽  
pp. 219-225
Author(s):  
J. Maeder ◽  
W. Rühl
Keyword(s):  
Sigma Models ◽  
Scaling Limits ◽  
Airy Functions ◽  
N Vector

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
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