4 papers · 1 filter
Locally seeded embeddings, and Ramsey numbers of bipartite graphs with sublinear bandwidth
Dylan J. Altschuler, Han Huang, Konstantin Tikhomirov
A seminal result of Lee asserts that the Ramsey number of any bipartite -degenerate graph satisfies . In particular, this bound applies to every b…
A combinatorial approach to nonlinear spectral gaps
Dylan J. Altschuler, Pandelis Dodos, Konstantin Tikhomirov +1
A seminal open question of Pisier and Mendel--Naor asks whether every degree-regular graph which satisfies the classical discrete Poincaré inequality for scalar functions, also sat…
On spectral outliers of inhomogeneous symmetric random matrices
Dylan J. Altschuler, Patrick Oliveira Santos, Konstantin Tikhomirov +1
Sharp conditions for the presence of spectral outliers are well understood for Wigner random matrices with iid entries. In the setting of inhomogeneous symmetric random matrices (i…
A note on the capacity of the binary perceptron
Dylan J. Altschuler, Konstantin Tikhomirov
Determining the capacity of the Binary Perceptron is a long-standing problem. Krauth and Mezard (1989) conjectured an explicit value of , approximately equal to .833, an…