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1. $L^p$-discrepancy and statistical independence of sequences

Creator:
Grabner, Peter J., Strauch, Oto, and Tichy, Robert F.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
sequences, statistical independence, discrepancy, and distribution functions
Language:
English
Description:
We characterize statistical independence of sequences by the $L^p$-discrepancy and the Wiener $L^p$-discrepancy. Furthermore, we find asymptotic information on the distribution of the $L^2$-discrepancy of sequences.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Discrepancy and eigenvalues of Cayley graphs

Creator:
Kohayakawa, Yoshiharu, Rödl, Vojtěch, and Schacht, Mathias
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
Matematika, matematika, mathematics, eigenvalue, discrepancy, quasirandomness, Cayley graph, 13, and 51
Language:
English
Description:
We consider quasirandom properties for Cayley graphs of finite abelian groups. We show that having uniform edge-distribution (i.e., small discrepancy) and having large eigenvalue gap are equivalent properties for such Cayley graphs, even if they are sparse. This affirmatively answers a question of Chung and Graham (2002) for the particular case of Cayley graphs of abelian groups, while in general the answer is negative., Yoshiharu Kohayakawa, Vojtěch Rödl, Mathias Schacht., and Obsahuje seznam literatury
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public