Finding blocks and other patterns in a random coloring of Z

By Heinrich Matzinger, Silke W. W. Rolles. 2006

47 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/d4031d96de5f9af6489f53ce1304e60991e3f900

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

On the singularity probability of random Bernoulli matrices (2005, methodology): “The proof of this theorem uses several ideas from [11, 17].”
Non-asymptotic theory of random matrices: extreme singular values (2010, background): “ost surely: pn := P(s min(A) = 0) → 0 as n → ∞. Later Kahn, Komlos and Szemeredi [43] proved that the singularity probability satisﬁes pn ≤ cn for some c ∈ (0,1). The base c was gradually improved in [78, 81], with the latest record of pn = (1/ √ 2+o(1))n obtained in [12]. It is conjectured that the”
Invertibility of random matrices: norm of the inverse (2005, methodology): “ILITY OF RANDOM MATRICES: NORM OF THE INVERSE 3 estimates, than those employed in [LPRT]. To obtainsuch estimates we use the method of Hal´asz, which lies in the foundation of the arguments of [KKS], [TV1], [TV2]. Let P(Ω) denote the probability of the event Ω, and let Eξ denote the expectation of t”
Inverse Littlewood-Offord theorems and the condition number of random discrete matrices (2005, methodology): “[10], [25], [26]).”
Random symmetric matrices are almost surely nonsingular (2005, methodology): “sults concerning the model An. In the rest of this section, it is more convenient to assume that the entries of An (and Qn) take value 1 and −1 (rather than 1 and 0). Under this condition, Tao and Vu [7] showed that almost surely detAn has absolute value n(1/2−o(1))n. We conjecture that a similar bo”
Random matrices: Universality of local eigenvalue statistics (2009, methodology): “g|det(Mn − √ nzI)|− 1 2 nlogn−n Z 2 −2 log|y−z|ρsc(y) dy| ≥ n1−c) = o(1) where the decay rate of o(1) is allowed to depend on z. Remark 35. A similar result was established for iid random matrices in [44] (see also [12] for a reﬁnement), based on controlling the distance from a random vector to a su”