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The dispersion measure (DM) of high-redshift $(z \gtrsim 6)$ transientobjects such as Fast Radio Bursts can be a powerful tool to probe theintergalactic medium during the Epoch of Reionization. In this paper, we studythe variance of the DMs of objects with the same redshift as a potential probeof the size distribution of ionized bubbles. We calculate the DM variance witha simple model with randomly-distributed spherical bubbles. It is found thatthe DM variance reflects the characteristics of the probability distribution ofthe bubble size. We find the variance can be measured precisely enough toobtain the information on the typical size with a few hundred sources at asingle redshift.

The variance of dispersion measure of high-redshift transient objects as a probe of ionized bubble size during reionization