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math.PR2025
Maximal Counts in the Stopped Occupancy Problem
Alexander Gnedin, Svante Janson, Yaakov Malinovsky
We revisit a version of the classic occupancy scheme, where balls are thrown until almost all boxes receive a given number of balls. Special cases are widely known as coupon-collec…
math.PR2025★ 3 cited
The generalized Alice HH vs Bob HT problem
Svante Janson, Mihai Nica, Simon Segert
In 2024, Daniel Litt posed a simple coinflip game pitting Alice's "Heads-Heads" vs Bob's "Heads-Tails": who is more likely to win if they score 1 point per occurrence of their subs…
math.PR2024
Better-than-average uniform random variables and Eulerian numbers, or: How many candidates should a voter approve?
Svante Janson, Warren D. Smith
Consider independent random numbers with a uniform distribution on . The number of them that exceed their mean is shown to have an Eulerian distribution, i.e., it is des…