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We provide the first tight bounds on the lower tail probability of the one point distribution of the KPZ equation with narrow wedge initial data.
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On the distribution of the length of the longest increasing subsequence of random permutations
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A. B. Soshnikov · 2000
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Optimal tail estimates for directed last passage site percolation with geometric random variables
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C. A. Tracy and H. Widom · 2002
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