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The spectrum of electromagnetic emission generated by relativistic electronsscattered on small-scale random magnetic fields, implied by current models ofthe magnetic field generation in the gamma-ray burst sources, is considered.The theory developed includes both perturbative and non-perturbative versionsand, therefore, suggests a general treatment of the radiation in arbitrarysmall-scale random field. It is shown that a general treatment of the randomnature of the small-scale magnetic field, as well as angular diffusion of theelectrons due to multiple scattering by magnetic inhomogeneities (i.e.,non-perturbative effects), give rise to a radiation spectrum that differssignificantly from so-called "jitter" spectrum. The spectrum of diffusivesynchrotron radiation seems to be consistent with the low energy spectral indexdistribution of the gamma-ray bursts.Comment: 15 pages, 2 figures, accepted for ApJ. Typo removed. More discussion  added. Wording adjusted to ApJ style: "errors" replaced with  "oversimplifications" or s

Diffusive Synchrotron Radiation from Relativistic Shocks in Gamma‐Ray Burst Sources