RT @ccanonne_: @AlmostSureMath ... captured by the quantity 1/‖p‖₄⁴. (Check that it does give n¾ for p uniform on {1,..,n}!) For the unifo…
@AlmostSureMath ... captured by the quantity 1/‖p‖₄⁴. (Check that it does give n¾ for p uniform on {1,..,n}!) For the uniform distribution we have very good bounds on this : see, for example, Theorem 2 of https://t.co/4YI7rJaTBl for the proba Pr[🍪(s,q)] o
Further Readings: 🔎 Kazuhiro Suzuki et al. (2006) – Birthday Paradox for Multi-collisions: https://t.co/6Jia8bHNam 🎓 Wiki: https://t.co/IPw6lC3xS9 📺 TED-Ed with David Knuffke: https://t.co/AIOBJ3zVjb 💡🧮🎂🔢💡🧮🎂🔢💡🧮🎂🔢💡 #birthdayparadox #birthdayattack #5e55
I'm sure it's old news to many, but hey. It's been a long day, and it's always good to have old news. Note that for s=2 we get roughly k²/n, so indeed we need k≳√n to have any reasonable chance of seeing a (2-way) collision. For a reference: e.g., https: