Abstract
AbstractWe introduce and study analogues of expander and hyperfinite graph sequences in the context of directed acyclic graphs, which we call ‘extender’ and ‘hypershallow’ graph sequences, respectively. Our main result is a probabilistic construction of non-hypershallow graph sequences.
Highlights
Explicitly introduced in [2]
In this article we study the analogues of hyperfinite and expander graph sequences in the context of oriented graphs, directed acyclic graphs
Our main result is a stochastic construction of graph sequences which are not hypershallow
Summary
3. If f is an N-valued random variable and α is its law, we define H(f ) := H(α). (a) If f and g are random variables with values in the same space Y , with laws α and β respectively, the law of f. It allows us to say the following: if f and g are N-valued random variables with laws α and β respectively, and (x, y) ∈ N2 is chosen according to the law α × β, either it is roughly as probable that x > y as it is that y > x, or the entropy of f ⊔ g is substantially larger than the average of the entropies of f and g. Let f and g be N-valued random variables with laws α and β, respectively.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
