It was recently discovered by Baik, Deift and Johansson [4] that the asymptotic distribution of the length of the longest increasing subsequence in a permutation chosen uniformly at random from Sn, properly centred and normalised, is the same as the asymptotic distribution of the largest eigenvalue of an n × n GUE random matrix, properly centred and normalised, as n → ∞. This distribution had e...

In a famous paper 8] Hammersley investigated the length L n of the longest increasing subsequence of a random n-permutation. Implicit in that paper is a certain one-dimensional continuous-space interacting particle process. By studying a hydrodynamical limit for Hammersley's process we show by fairly \soft" arguments that limn ?1=2 EL n = 2. This is a known result, but previous proofs (Vershik-...

We compute the limit distribution for the (centered and scaled) length of the longest increasing subsequence of random colored permutations. The limit distribution function is a power of that for usual random permutations computed recently by Baik, Deift, and Johansson (math.CO/9810105). In the two–colored case our method provides a different proof of a similar result by Tracy and Widom about t...

Connections between longest increasing subsequences in random permutations and eigenvalues of random matrices with complex entries have been intensely studied. This note applies properties of random elements of the finite general linear group to obtain results about the longest increasing subsequence in non-uniform random permutations.

The catalyst Pt-Ta supported on 7-alumina was prepared by impregnation with solution containing compoundsof II21K1.0. and Ta205 The Pt concentration was kept constant at 0.2 vet% while the concentration of thetantalum was 0,4 wt%. The activity and selectivity of catalyst were determined under conditions at 450-500 °Cand 15-30 atm.. with molar ratio H2/C[H,e5 and WH=1.5mL/h for converted n-hepta...

Electron- and hole-transfer reactions are studied in colloidal InP quantum dots (QDs). Photoluminescence quenching and time-resolved transient absorption (TA) measurements are utilized to examine hole transfer from photoexcited InP QDs to the hole acceptor N,N,N',N'-tetramethyl-p-phenylenediamine (TMPD) and electron transfer to nanocrystalline titanium dioxide (TiO2) films. Core-confined holes ...