Fooling pairs are one of the standard methods for proving lower bounds for deterministic two-player communication complexity. We study fooling pairs in the context of randomized communication complexity.
We show that every fooling pair induces far away distributions on transcripts of private-coin protocols. We then conclude that the private-coin randomized $\varepsilon$-error communication complexity of a function $f$ with a fooling set $\mathcal{S}$ is at least order $\log \frac{\log |\mathcal{S}|}{\varepsilon}$. This is tight, for example, for the equality and greater-than functions.

Corrected some minor errors.

Fooling pairs are one of the standard methods for proving lower bounds for deterministic two-player communication complexity. We study fooling pairs in the context of randomized communication complexity.
We show that every fooling pair induces far away distributions on transcripts of private-coin protocols. We then conclude that the private-coin randomized $\varepsilon$-error communication complexity of a function $f$ with a fooling set $\mathcal{S}$ is at least order $\log \frac{\log |\mathcal{S}|}{\varepsilon}$. This is tight, for example, for the equality and greater-than functions.