Permanent problem IDPPL 176
Probability
For two independent uniform N-point samples in the unit square and exponents α₁,α₂ with 1/α₁+1/α₂=1/2, prove Talagrand’s universal-probability matching bounds; either special target (∞,2) or (4,4) earns the full prize.
For two independent uniform N-point samples in the unit square and exponents α₁,α₂ with 1/α₁+1/α₂=1/2, prove Talagrand’s universal-probability matching bounds; either special target (∞,2) or (4,4) earns the full prize.
A proof of the full statement or either explicitly listed special case earns the full prize under Talagrand’s general conditions.
The 2021 book still presents the 2D problem as open; the cash PDF dates to 2013, so reconfirm payout before reliance.