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We consider a standard two-source model for uniform common randomness (UCR)generation, in which Alice and Bob observe independent and identicallydistributed (i.i.d.) samples of a correlated finite source and where Alice isallowed to send information to Bob over an arbitrary single-user channel. Westudy the \(\boldsymbol{\epsilon}\)-UCR capacity for the proposed model,defined as the maximum common randomness rate one can achieve such that theprobability that Alice and Bob do not agree on a common uniform or nearlyuniform random variable does not exceed \(\boldsymbol{\epsilon}.\)  We establish a lower and an upper bound on the \(\boldsymbol{\epsilon}\)-UCRcapacity using the bounds on the \(\boldsymbol{\epsilon}\)-transmissioncapacity proved by Verd\'u and Han for arbitrary point-to-point channels.

A Lower and Upper Bound on the Epsilon-Uniform Common Randomness Capacity