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The problem of predecessors on spanning trees · Around

2010

The problem of predecessors on spanning trees

Poghosyan, V. S., Priezzhev, V. B.

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We consider the equiprobable distribution of spanning trees on the square lattice.

All bonds of each tree can be oriented uniquely with respect to an arbitrary chosen site called the root.
The problem of predecessors is finding the probability that a path along the oriented bonds passes sequentially fixed sites $i$ and $j$.
The conformal field theory for the Potts model predicts the fractal dimension of the path to be 5/4.

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