scholarly journals Joint scaling limit of site percolation on random triangulations in the metric and peanosphere sense

2021 ◽  
Vol 26 (none) ◽  
Author(s):  
Ewain Gwynne ◽  
Nina Holden ◽  
Xin Sun
Keyword(s):  
Scaling Limit ◽  
Site Percolation

Site percolation : Frontier curvature of clusters

1973 ◽  
Vol 34 (5-6) ◽  
pp. 341-344 ◽  
Author(s):  
H. Ottavi ◽  
J.P. Gayda
Keyword(s):  
Site Percolation

Improvement in Gate Dielectric Quality of Ultra Thin a: SiN:H MNS Capacitor by Hydrogen Etching of the Substrate

2002 ◽  
Vol 716 ◽  
Author(s):  
Parag C. Waghmare ◽  
Samadhan B. Patil ◽  
Rajiv O. Dusane ◽  
V.Ramgopal Rao
Keyword(s):  
Silicon Nitride ◽  
Gate Dielectric ◽  
Substrate Surface ◽  
Scaling Limit ◽  
Tunneling Current ◽  
Chemical Vapor ◽  
Poor Performance ◽  
State Density ◽  
Direct Tunneling Current

AbstractTo extend the scaling limit of thermal SiO2, in the ultra thin regime when the direct tunneling current becomes significant, members of our group embarked on a program to explore the potential of silicon nitride as an alternative gate dielectric. Silicon nitride can be deposited using several CVD methods and its properties significantly depend on the method of deposition. Although these CVD methods can give good physical properties, the electrical properties of devices made with CVD silicon nitride show very poor performance related to very poor interface, poor stability, presence of large quantity of bulk traps and high gate leakage current. We have employed the rather newly developed Hot Wire Chemical Vapor Deposition (HWCVD) technique to develop the a:SiN:H material. From the results of large number of optimization experiments we propose the atomic hydrogen of the substrate surface prior to deposition to improve the quality of gate dielectric. Our preliminary results of these efforts show a five times improvement in the fixed charges and interface state density.

scholarly journals Scaling limit of the Z2 invariant inhomogeneous six-vertex model

2021 ◽  
Vol 965 ◽  
pp. 115337 ◽  
Author(s):  
Vladimir V. Bazhanov ◽  
Gleb A. Kotousov ◽  
Sergii M. Koval ◽  
Sergei L. Lukyanov
Keyword(s):  
Scaling Limit ◽  
Vertex Model

scholarly journals The bead process for beta ensembles

2021 ◽  
Author(s):  
Joseph Najnudel ◽  
Bálint Virág
Keyword(s):  
Point Processes ◽  
Scaling Limit ◽  
Companion Paper ◽  
Point Counting ◽  
Infinite Dimensional ◽  
Transition Mechanism ◽  
Beta Ensemble ◽  
Beta Ensembles ◽  
Orthogonal Ensembles ◽  
Gaussian Beta Ensembles

AbstractThe bead process introduced by Boutillier is a countable interlacing of the $${\text {Sine}}_2$$ Sine 2 point processes. We construct the bead process for general $${\text {Sine}}_{\beta }$$ Sine β processes as an infinite dimensional Markov chain whose transition mechanism is explicitly described. We show that this process is the microscopic scaling limit in the bulk of the Hermite $$\beta $$ β corner process introduced by Gorin and Shkolnikov, generalizing the process of the minors of the Gaussian Unitary and Orthogonal Ensembles. In order to prove our results, we use bounds on the variance of the point counting of the circular and the Gaussian beta ensembles, proven in a companion paper (Najnudel and Virág in Some estimates on the point counting of the Circular and the Gaussian Beta Ensemble, 2019).

scholarly journals Characters of irrelevant deformations

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Shouvik Datta ◽  
Yunfeng Jiang
Keyword(s):  
Deformation Parameter ◽  
Central Charge ◽  
Scaling Limit ◽  
Small Deformation ◽  
State Dependent ◽  
Dependent Change ◽  
Left And Right ◽  
Double Scaling Limit

Abstract We analyse the $$ T\overline{T} $$ T T ¯ deformation of 2d CFTs in a special double-scaling limit, of large central charge and small deformation parameter. In particular, we derive closed formulae for the deformation of the product of left and right moving CFT characters on the torus. It is shown that the 1/c contribution takes the same form as that of a CFT, but with rescalings of the modular parameter reflecting a state-dependent change of coordinates. We also extend the analysis for more general deformations that involve $$ T\overline{T} $$ T T ¯ , $$ J\overline{T} $$ J T ¯ and $$ T\overline{J} $$ T J ¯ simultaneously. We comment on the implications of our results for holographic proposals of irrelevant deformations.

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