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The lasing threshold is studied of a multi-mode chaotic cavity (linear size D>> wavelength \lambda) coupled to the outside through a small hole (linear sized << \lambda). For sufficiently weak absorption by the boundaries, thestatistical distribution of the threshold is wide, its mean value being muchless than the pumping rate needed to compensate the average loss. The averagenumber N_{nc} >> 1 of non-competing excited modes is proportional to the squareroot of the pumping rate. We use the classical model of spatial hole burning toaccount for mode competition and find a reduction in the average number ofexcited modes to N =3^{1/3} N_{nc}^{2/3}.Comment: 6 pages, RevTeX, 3 figures. Discussion of effects of non-zero  resistivity in the boundaries is adde

Lasing threshold and mode competition in chaotic cavities