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Approximate confidence limits on the temperature of the hottest hotspot expected on the microwave sky are derived under the condition that the coherence angle of the temperature fluctuations is a very small fraction of the total sky. We apply the result to temperature anisotropies expected in galaxy formation models where the universe is dominated by cold dark matter and discuss its possible use for discriminating between high peaks in system noise and true sky fluctuations.
Peter Coles (Tue,) studied this question.