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Let g 1 (ω), g 2 (ω), . . . , gn(ω) be independent and normally distributed random variables with mean zero and variance one. We show that, for large values of n, the expected number of times the random hyperbolic polynomial (1) , but decreases steadily as O(L) increases in magnitude and ultimately becomes negligible when n −1 log L/ √ n → ∞. 2010 AMS Mathematics subject classification. Primary 60H99, Secondary 26C99.doi:10.1216/rmj-2015-45-4-1197 fatcat:3ipcukmd3feazeshnehdd527ue