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Robert Burton coauthored the transfer-impedance analysis of uniform spanning trees with Robin Pemantle. Their original paper verifies this byline.^[ref]

The method computes probabilities for small collections of edges from determinants, even when the graph is large. The relevant matrix entries depend on global electrical information, so a small determinant does not mean the problem is entirely local. This distinction is essential in extending the calculations to infinite periodic graphs.^[ref]

Robin Pemantle studies probability theory and random combinatorial structures. With Robert Burton, he developed methods for computing local probabilities in uniform spanning trees using electrical transfer impedances.^[ref]

The probability that several specified edges occur is a determinant of a small transfer matrix. This avoids enumerating all trees and relates joint edge events to Green's functions and network currents. Their work also applies these methods to domino tilings and entropy.^[ref]