We present CARMA 1.3 mm continuum observations of the T Tauri star LkCa 15,which resolve the circumstellar dust continuum emission on angular scales between 0.2-3 arcsec, corresponding to 28-420 AU at the distance of the star. The observations resolve the inner gap in the dust emission and reveal an asymmetric dust distribution in the outer disk. (Abridge) We calculate that 90% of the dust emission arises from an azimuthally symmetric ring that contains about 5x10^{-4} M_sun of dust. A low surface-brightness tail that extends to the northwest out to a radius of about 300 AU contains the remaining 10% of the observed continuum emission. The ring is modeled with a rather flat surface density profile between 40 and 120 AU, while the inner cavity is consistent with either a sharp drop of the 1.3 mm dust optical depth at about 42 AU or a smooth inward decrease between 3 and 85 AU. (Abridge). Within 40 AU, the observations constrain the amount of dust between 10^{-6} and 7 Earth masses, where the minimum and maximum limits are set by the near-IR SED modeling and by the mm-wave observations of the dust emission respectively. In addition, we confirm the discrepancy in the outer disk radius inferred from the dust and gas, which corresponds to 150 AU and 900 AU respectively. We cannot reconcile this difference by adopting an exponentially tapered surface density profile as suggested for other systems, but we instead suggest that the gas surface density in the outer disk decreases less steeply than that predicted by model fits to the dust continuum emission. The lack of continuum emission at radii lager than 120 AU suggests a drop of at least a factor of 5 in the dust-to-gas ratio, or in the dust opacity. We show that a sharp dust opacity drop of this magnitude is consistent with a radial variation of the grain size distribution as predicted by existing grain growth models.
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