REVIEW 1 cited by
On binomial sums, additive energies, and lazy random walks
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
abstract
We establish a sharp estimate for $k$-additive energies of subsets of the discrete hypercube conjectured by de Dios Pont, Greenfeld, Ivanisvili, and Madrid in arXiv:2112.09352, which generalizes a result by Kane and Tao. This note proves the only missing ingredient, which is an elementary inequality for real numbers, previously verified only for $k\leq100$. We also give an interpretation of this inequality in terms of a lazy non-symmetric simple random walk on the integer lattice.
Forward citations
Cited by 1 Pith paper
-
Optimal Young's convolutions inequality and its reverse form on the hypercube
Sharp Young's convolution inequality and its reverse on {0,1}^d are proved, with optimal diagonal exponent p_r = 2r/log_2(2+2^r).
Discussion (0). Continue with ORCID to comment.