On Weierstrass-like functions and random recurrent sets

1989 ◽  
Vol 106 (2) ◽  
pp. 325-342 ◽  
Author(s):  
Tim Bedford
Keyword(s):  
Hausdorff Dimension ◽  
Random Matrix ◽  
Hausdorff Dimensions ◽  
Random Matrix Products ◽  
Matrix Products ◽  
Recurrent Set

AbstractA construction of Weierstrass-like functions using recurrent sets is described, and the Hausdorff dimensions of the graphs computed. An important part of the proof is the notion of a globally random recurrent set. The Hausdorff dimension of a class of such sets is calculated using techniques of random matrix products.

scholarly journals Random matrix products: Universality and least singular values

2020 ◽  
Vol 48 (3) ◽  
pp. 1372-1410
Author(s):  
Phil Kopel ◽  
Sean O’Rourke ◽  
Van Vu
Keyword(s):  
Random Matrix ◽  
Singular Values ◽  
Random Matrix Products ◽  
Matrix Products
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