L 2-lower bounds for a special class of random walks

1995 ◽  
Vol 101 (2) ◽  
pp. 277-289 ◽  
Author(s):  
Ursula Porod
1987 ◽  
Vol 35 (1) ◽  
pp. 49-57
Author(s):  
Choon Peng Tan

Lower bounds for the tau coefficients and operator norms are derived by using composite matrix norms. For a special class of matrices B, our bounds on ‖B‖p (the operator norm of B induced by the ℓp norm) improve upon a general class of Maitre (1967) bounds for p ≥ 2.


Author(s):  
A. R. Balasubramanian ◽  
Javier Esparza ◽  
Mikhail Raskin

AbstractIn rendez-vous protocols an arbitrarily large number of indistinguishable finite-state agents interact in pairs. The cut-off problem asks if there exists a number B such that all initial configurations of the protocol with at least B agents in a given initial state can reach a final configuration with all agents in a given final state. In a recent paper [17], Horn and Sangnier prove that the cut-off problem is equivalent to the Petri net reachability problem for protocols with a leader, and in "Image missing" for leaderless protocols. Further, for the special class of symmetric protocols they reduce these bounds to "Image missing" and "Image missing" , respectively. The problem of lowering these upper bounds or finding matching lower bounds is left open. We show that the cut-off problem is "Image missing" -complete for leaderless protocols, "Image missing" -complete for symmetric protocols with a leader, and in "Image missing" for leaderless symmetric protocols, thereby solving all the problems left open in [17].


1994 ◽  
Vol 49 (10) ◽  
pp. 973-976
Author(s):  
Tetsuo Morikawa

Abstract It is possible to regard two polygonal skeletons as the same in a special class of carbocyclic and heterocyclic compounds, if the one is reducible to the other by means of the contraction of cyclic subskeletons, and if the numbers of conjugated patterns in them are equal to each other. In such polygonal skeletons, three forms of cyclic subskeletons are defined; the one is called “alternate”, and the others, involving the one called “inclusive”, have a path (b, b), where (b) is a conjugated vertex connecting with three vertices. Successive eliminations of the cyclic subskeletons enable to estimate the upper and lower bounds for the number of conjugated patterns in a given polygonal skeleton.


2015 ◽  
Vol 9 (3) ◽  
pp. 711-735 ◽  
Author(s):  
Sébastien Gouëzel ◽  
Frédéric Mathéus ◽  
François Maucourant

1991 ◽  
Vol 34 (1) ◽  
pp. 3-11 ◽  
Author(s):  
Toshiaki Adachi

AbstractWe investigate some properties of spherical means on the universal covering space of a compact Riemannian manifold. If the fundamental group is amenable then the greatest lower bounds of the spectrum of spherical Laplacians are equal to zero. If the fundamental group is nontransient so are geodesic random walks. We also give an isoperimetric inequality for spherical means.


10.37236/439 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Tobias Friedrich ◽  
Thomas Sauerwald

The rotor router model is a popular deterministic analogue of a random walk on a graph. Instead of moving to a random neighbor, the neighbors are served in a fixed order. We examine how quickly this "deterministic random walk" covers all vertices (or all edges). We present general techniques to derive upper bounds for the vertex and edge cover time and derive matching lower bounds for several important graph classes. Depending on the topology, the deterministic random walk can be asymptotically faster, slower or equally fast as the classic random walk. We also examine the short term behavior of deterministic random walks, that is, the time to visit a fixed small number of vertices or edges.


Author(s):  
Mikhail Menshikov ◽  
Serguei Popov ◽  
Andrew Wade
Keyword(s):  

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