Locality Bounds for Sampling Hamming Slices
Anthony Ostuni (UCSD)
Monday, April 29th 2024, 2-3pm
Abstract:
Spurred by the influential work of Viola (Journal of Computing 2012), the past decade has witnessed an active line of research into the complexity of (approximately) sampling distributions, in contrast to the traditional focus on the complexity of computing functions. I will discuss recent work with Daniel M. Kane and Kewen Wu that builds upon and makes explicit earlier implicit results of Viola to provide superconstant lower bounds on the locality of Boolean functions approximately sampling the uniform distribution over binary strings of particular Hamming weights, both exactly and modulo an integer, answering questions of Viola (Journal of Computing 2012) and Filmus, Leigh, Riazanov, and Sokolov (RANDOM 2023). Applications to data structure lower bounds and quantum-classical separations will be covered.
Speaker information:
Anthony Ostuni is a third-year PhD student, advised by Daniel M. Kane and Shachar Lovett. He is interested in complexity theory and combinatorics.