Uniform boundedness of critical crossing probabilities implies hyperscaling
نویسندگان
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
Microsoft Technical Report MSR-TR-98-26 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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عنوان ژورنال:
- Random Struct. Algorithms
دوره 15 شماره
صفحات -
تاریخ انتشار 1999