48,272 research outputs found
Self-regulation in the Bolker-Pacala model
The Markov dynamics is studied of an infinite system of point entities placed
in \mathds{R}^d, in which the constituents disperse and die, also due to
competition. Assuming that the dispersal and competition kernels are continuous
and integrable we show that the evolution of states of this model preserves
their sub-Poissonicity, and hence the local self-regulation (suppression of
clustering) takes place. Upper bounds for the correlation functions of all
orders are also obtained for both long and short dispersals, and for all values
of the intrinsic mortality rate.Comment: arXiv admin note: substantial text overlap with arXiv:1702.0292
Gibbs random fields with unbounded spins on unbounded degree graphs
Gibbs random fields corresponding to systems of real-valued spins (e.g.
systems of interacting anharmonic oscillators) indexed by the vertices of
unbounded degree graphs with a certain summability property are constructed. It
is proven that the set of tempered Gibbs random fields is non-void and weakly
compact, and that they obey uniform exponential integrability estimates. In the
second part of the paper, a class of graphs is described in which the mentioned
summability is obtained as a consequence of a property, by virtue of which
vertices of large degree are located at large distances from each other. The
latter is a stronger version of a metric property, introduced in [Bassalygo, L.
A. and Dobrushin, R. L. (1986). \textrm{Uniqueness of a Gibbs field with a
random potential--an elementary approach.}\textit{Theory Probab. Appl.} {\bf
31} 572--589]
Computations on Nondeterministic Cellular Automata
The work is concerned with the trade-offs between the dimension and the time
and space complexity of computations on nondeterministic cellular automata. It
is proved, that
1). Every NCA \Cal A of dimension , computing a predicate with time
complexity T(n) and space complexity S(n) can be simulated by -dimensional
NCA with time and space complexity and
by -dimensional NCA with time and space complexity .
2) For any predicate and integer if \Cal A is a fastest
-dimensional NCA computing with time complexity T(n) and space
complexity S(n), then .
3). If is time complexity of a fastest -dimensional NCA
computing predicate then T_{r+1,P} &=O((T_{r,P})^{1-r/(r+1)^2}),
T_{r-1,P} &=O((T_{r,P})^{1+2/r}). Similar problems for deterministic CA are
discussed.Comment: 18 pages in AmsTex, 3 figures in PostScrip
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