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pro vyhledávání: '"Grimmett, G. R."'
The following paper is part of the authors' response to an invitation from the Constitutional Affairs Committee (AFCO) of the European Parliament to advise on mathematical methods for the allocation of Parliamentary seats between the 27 Member States
Externí odkaz:
http://arxiv.org/abs/1710.03820
We prove the existence of a (random) Lipschitz function $F : \Z^{d-1}\to\Z^+$ such that, for every $x \in \Z^{d-1}$, the site $(x,F(x))$ is open in a site percolation process on $\Z^{d}$. The Lipschitz constant may be taken to be 1 when the parameter
Externí odkaz:
http://arxiv.org/abs/0911.3384
Autor:
Björnberg, J. E., Grimmett, G. R.
An analysis is presented of the phase transition of the quantum Ising model with transverse field on the d-dimensional hypercubic lattice. It is shown that there is a unique sharp transition. The value of the critical point is calculated rigorously i
Externí odkaz:
http://arxiv.org/abs/0901.0328
Autor:
Graham, B. T., Grimmett, G. R.
The so-called diluted-random-cluster model may be viewed as a random-cluster representation of the Blume--Capel model. It has three parameters, a vertex parameter $a$, an edge parameter $p$, and a cluster weighting factor $q$. Stochastic comparisons
Externí odkaz:
http://arxiv.org/abs/math/0512523
Autor:
Graham, B. T., Grimmett, G. R.
The influence theorem for product measures on the discrete space {0,1}^N may be extended to probability measures with the property of monotonicity (which is equivalent to `strong positive-association'). Corresponding results are valid for probability
Externí odkaz:
http://arxiv.org/abs/math/0505057
Autor:
Grimmett, G. R., Winkler, S. N.
We consider three probability measures on subsets of edges of a given finite graph $G$, namely those which govern, respectively, a uniform forest, a uniform spanning tree, and a uniform connected subgraph. A conjecture concerning the negative associa
Externí odkaz:
http://arxiv.org/abs/math/0302185
Autor:
Grimmett, G. R., Stacey, A. M.
Publikováno v:
The Annals of Probability, 1998 Oct 01. 26(4), 1788-1812.
Externí odkaz:
https://www.jstor.org/stable/2652790
Autor:
Graham, B. T., Grimmett, G. R.
Publikováno v:
The Annals of Probability, 2006 Sep 01. 34(5), 1726-1745.
Externí odkaz:
https://www.jstor.org/stable/25449932