Characterizing a cosmic string with the statistics of string lensing

The deep imaging of the field of an observed lensing event by a cosmic string reveals many additional lensing events. We study the statistics of such string lensing. We derive explicit expressions for the distributions of image separations of lensing by a cosmic string and point out that they are quite sensitive to parameters which characterize the cosmic string, such as the redshift and tension of the cosmic string. Thus the statistics of string lensing events add new important information on the cosmic string which cannot be obtained from the detailed investigation of one lensing event.