SummaryLet Sn=X1+X2+⋯+Xnbe the sum of i.i.d.r.v.-s, EX1=0, EX12=1, and let Tn= Y1+Y2+⋯+Ynbe the sum of independent standard normal variables. Strassen proved in [14] that if X1 has a finite fourth… Expand

We show that with probability 1-o(1)all eigenvalues belong to the above intervalI if μ=0, while in case μ>0 only the largest eigenvalue λ1 is outsideI.Expand

Szemer\''edi''s Regularity Lemma is an important tool in discrete mathematics. It says that, in some sense, all graphs can be approximated by random-looking graphs. Therefore the lemma helps in… Expand

We describe a data structure for representing a set of n items from a universe of m items, which uses space n+o(n) and accommodates membership queries in constant time.Expand

This is the fixed version of an article made available by an organization that acts as a publisher by formally and exclusively declaring the article "published". If it is an "early release" article… Expand

We report some progress on the old problem of estimating the probability, Pn, that a random n× n ± 1 matrix is singular: Theorem. There is a positive constant ε for which Pn < (1− ε)n. This is a… Expand

Paul Seymour conjectured that any graphG of ordern and minimum degree of at leastk/k+1n contains thekth power of a Hamiltonian cycle. Here, we prove this conjecture for sufficiently largen.