منابع مشابه
The Measurable Kesten Theorem
We give an explicit bound on the spectral radius in terms of the densities of short cycles in finite d-regular graphs. It follows that the a finite d-regular Ramanujan graph G contains a negligible number of cycles of size less than c log log |G|. We prove that infinite d-regular Ramanujan unimodular random graphs are trees. Through Benjamini-Schramm convergence this leads to the following rigi...
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The uniqueness of the infinite open cluster in the setting of bond percolation on the square grid was proven by Harris in 1960 [6]. As shown by Fisher in 1961 [4], Harris’ proof can be extended to include site percolation on the square grid. Aizenman, Kesten, and Newman [1] show that this fact is true in a much more general setting, as well. Let Λ be a connected, infinite, locally-finite, verte...
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A short proof of the Harris-Kesten result that the critical probability for bond percolation in the planar square lattice is 1/2 was given in [1], using a sharp threshold result of Friedgut and Kalai. Here we point out that a key part of this proof may be replaced by an argument of Russo [6] from 1982, using his approximate zero-one law in place of the Friedgut-Kalai result. Russo’s paper gave ...
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Policing constantly places its practitioners in situations in which good ends can be achieved by dirty means. When the ends to be achieved are urgent and unquestionably good and only a dirty means will work to achieve them, the policeman faces a genuine moral dilemma. A genuine moral dilemma is a situation from which one cannot emerge innocent no matter what one does-employ a dirty means, emplo...
متن کاملHarry Beal Torrey , Matthew
I t is now 16 years since Nowikoff (1908) accelerated the division rate of Paramecium by adding thyroid gland to his cultures. Later , Shumway (1914) reached the same conclusion after a series of more critical and painstaking experiments, and in the following year Budington and Harvey (1915) showed tha t thyroids from various vertebrates would produce similar results. Still later, Shumway (1917...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2021
ISSN: ['0178-8051', '1432-2064']
DOI: https://doi.org/10.1007/s00440-021-01077-x