Noncommutative Deformations of Thick Points

2018 ◽  
Author(s):  
Olav Arnfinn Laudal
Keyword(s):  
Thick Points

scholarly journals The Dimension of the Boundary of a Liouville Quantum Gravity Metric Ball

2020 ◽  
Vol 378 (1) ◽  
pp. 625-689 ◽  
Author(s):  
Ewain Gwynne
Keyword(s):  
Hausdorff Dimension ◽  
Quantum Gravity ◽  
Free Field ◽  
Gaussian Free Field ◽  
Hausdorff Dimensions ◽  
Thick Points

Abstract Let $$\gamma \in (0,2)$$ γ ∈ ( 0 , 2 ) , let h be the planar Gaussian free field, and consider the $$\gamma $$ γ -Liouville quantum gravity (LQG) metric associated with h. We show that the essential supremum of the Hausdorff dimension of the boundary of a $$\gamma $$ γ -LQG metric ball with respect to the Euclidean (resp. $$\gamma $$ γ -LQG) metric is $$2 - \frac{\gamma }{d_\gamma }\left( \frac{2}{\gamma } + \frac{\gamma }{2} \right) + \frac{\gamma ^2}{2d_\gamma ^2}$$ 2 - γ d γ 2 γ + γ 2 + γ 2 2 d γ 2 (resp. $$d_\gamma -1$$ d γ - 1 ), where $$d_\gamma $$ d γ is the Hausdorff dimension of the whole plane with respect to the $$\gamma $$ γ -LQG metric. For $$\gamma = \sqrt{8/3}$$ γ = 8 / 3 , in which case $$d_{\sqrt{8/3}}=4$$ d 8 / 3 = 4 , we get that the essential supremum of Euclidean (resp. $$\sqrt{8/3}$$ 8 / 3 -LQG) dimension of a $$\sqrt{8/3}$$ 8 / 3 -LQG ball boundary is 5/4 (resp. 3). We also compute the essential suprema of the Euclidean and $$\gamma $$ γ -LQG Hausdorff dimensions of the intersection of a $$\gamma $$ γ -LQG ball boundary with the set of metric $$\alpha $$ α -thick points of the field h for each $$\alpha \in \mathbb R$$ α ∈ R . Our results show that the set of $$\gamma /d_\gamma $$ γ / d γ -thick points on the ball boundary has full Euclidean dimension and the set of $$\gamma $$ γ -thick points on the ball boundary has full $$\gamma $$ γ -LQG dimension.

scholarly journals Thick points of the Gaussian free field

2010 ◽  
Vol 38 (2) ◽  
pp. 896-926 ◽  
Author(s):  
Xiaoyu Hu ◽  
Jason Miller ◽  
Yuval Peres
Keyword(s):  
Free Field ◽  
Gaussian Free Field ◽  
Thick Points

scholarly journals Thick points for planar Brownian motion and the Erdős-Taylor conjecture on random walk

2001 ◽  
Vol 186 (2) ◽  
pp. 239-270 ◽  
Author(s):  
Amir Dembo ◽  
Yuval Peres ◽  
Jay Rosen ◽  
Ofer Zeitouni
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Planar Brownian Motion ◽  
Thick Points

scholarly journals Thick Points for Transient Symmetric Stable Processes

1999 ◽  
Vol 4 (0) ◽  
Author(s):  
Amir Dembo ◽  
Yuval Peres ◽  
Jay Rosen ◽  
Ofer Zeitouni
Keyword(s):  
Stable Processes ◽  
Symmetric Stable Processes ◽  
Thick Points

scholarly journals Distributions in spaces with thick points

2013 ◽  
Vol 401 (2) ◽  
pp. 821-835 ◽  
Author(s):  
Yunyun Yang ◽  
Ricardo Estrada
Keyword(s):  
Thick Points

scholarly journals Thick points for a Gaussian Free Field in 4 dimensions

2015 ◽  
Vol 125 (6) ◽  
pp. 2383-2404 ◽  
Author(s):  
Alessandra Cipriani ◽  
Rajat Subhra Hazra
Keyword(s):  
Free Field ◽  
Gaussian Free Field ◽  
Thick Points

scholarly journals Brownian intersection local times: Upper tail asymptotics and thick points

2002 ◽  
Vol 30 (4) ◽  
pp. 1605-1656 ◽  
Author(s):  
Wolfgang König ◽  
Peter Mörters
Keyword(s):  
Local Times ◽  
Tail Asymptotics ◽  
Thick Points ◽  
Intersection Local Times

Thin and thick points for branching measure on a Galton–Watson tree

2002 ◽  
Vol 58 (1) ◽  
pp. 13-22 ◽  
Author(s):  
Peter Mörters ◽  
Narn-Rueih Shieh
Keyword(s):  
Thick Points
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