Microsoft Technical Report MSR-TR-98-26 UNIFORM BOUNDEDNESS OF CRITICAL CROSSING PROBABILITIES IMPLIES HYPERSCALING
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چکیده
We consider bond percolation on the d-dimensional hypercubic lattice. Assuming the existence of a single critical exponent, the exponent ρ describing the decay rate of point-to-plane crossings at the critical point, we prove that hyperscaling holds whenever critical rectangle crossing probabilities are uniformly bounded away from 1.
منابع مشابه
Uniform boundedness of critical crossing probabilities implies hyperscaling
We consider bond percolation on the d-dimensional hypercubic lattice. Assuming the existence of a single critical exponent, the exponent ρ describing the decay rate of point-to-plane crossings at the critical point, we prove that hyperscaling holds whenever critical rectangle crossing probabilities are uniformly bounded away from 1.
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تاریخ انتشار 1998