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We propose to use degree-scale angular clustering of fast radio bursts (FRBs)to identify their origin and the host galaxy population. We study theinformation content in autocorrelation of the angular positions and dispersionmeasures (DM) and in cross-correlation with galaxies. We show that thecross-correlation with Sloan Digital Sky Survey (SDSS) galaxies will placestringent constraints on the mean physical quantities associated with FRBs. If$\sim$10,000 FRBs are detected with $\lesssim \rm deg$ resolution in the SDSSfield, the clustering analysis with the intrinsic DM scatter of $100\, {\rmpc}/{\rm cm}^3$ can constrain the global abundance of free electrons at $z\lt1$and the large-scale bias of FRB host galaxies (the statistical relation betweenthe distribution of host galaxies and cosmic matter density field) withfractional errors (with a $68\%$ confidence level) of $\sim10\%$ and$\sim20\%$, respectively. The mean near-source dispersion measure and the delaytime distribution of FRB rates relative to the global star forming rate can bealso determined by combining the clustering and the probability distributionfunction of DM. Our approach will be complementary to high-resolution ($\ll{\rm deg}$) event localization using e.g., VLA and VLBI for identifying theorigin of FRBs and the source environment. We strongly encourage futureobservational programs such as CHIME, UTMOST, and HIRAX to survey FRBs in theSDSS field.

Large-scale clustering as a probe of the origin and the host environment of fast radio bursts