Local tail bounds for polynomials on the discrete cube

Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel. Email: boaz.klartag@weizmann.ac.il. Supported by a grant from the Israel Science Foundation (ISF). School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, UK. Email: a.sodin@qmul.ac.uk. Supported in part by a Royal Society Wolfson Research Merit Award (WM170012), and a Philip Leverhulme Prize of the Leverhulme Trust (PLP-2020-064).