EFM transports samples between two distributions by following the electric field generated by placing the distributions on opposite plates of a capacitor.
Since P(·) and Q(·) have compact supports and the total charge related to the system of the two plates is zero, by Lemma A.6, these tubes must start from P(·) almost surely
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Field Matching: an Electrostatic Paradigm to Generate and Transfer Data
EFM transports samples between two distributions by following the electric field generated by placing the distributions on opposite plates of a capacitor.