  We consider statistics of a planar ideal polymer loop of length $L$ in a
large deviation regime, when a gyration radius, $R_g$, is slightly less than
the radius of a fully inflated ring, $\frac{L}{2\pi}$. Specifically, we study
analytically and via off-lattice Monte-Carlo simulations relative fluctuations
of chain monomers in ensemble of Brownian loops. We have shown that these
fluctuations in the regime with fixed large gyration radius are Gaussian with
the critical exponent $\gamma = \frac{1}{2}$. However, if we insert inside the
inflated loop the impenetrable disc of radius $R_d=R_g$, the fluctuations
become non-Gaussian with the critical exponent $\gamma=\frac{1}{3}$ typical for
the Kardar-Parisi-Zhang universality class.
