The Length of the Longest Increasing Subsequence of a Random Mallows Permutation
نویسنده
چکیده
The Mallows measure on the symmetric group Sn is the probability measure such that each permutation has probability proportional to q raised to the power of the number of inversions, where q is a positive parameter and the number of inversions of π is equal to the number of pairs i < j such that πi > πj . We prove a weak law of large numbers for the length of the longest increasing subsequence for Mallows distributed random permutations, in the limit that n→∞ and q → 1 in such a way that n(1− q) has a limit in R.
منابع مشابه
On the Length of the Longest Increasing Subsequence in a Random Permutation
Complementing the results claiming that the maximal length L n of an increasing subsequence in a random permutation of f1; 2; : : : ; ng is highly concentrated, we show that L n is not concentrated in a short interval: sup l P(l L n l + n 1=16 log ?3=8 n) ! 0 as n ! 1.
متن کاملOn the length of the longest subsequence avoiding an arbitrary pattern in a random permutation
We consider the distribution of the length of the longest subsequence avoiding an arbitrary pattern, π, in a random permutation of length n. The well-studied case of a longest increasing subsequence corresponds to π = 21. We show that there is some constant cπ such that as n → ∞ the mean value of this length is asymptotic to 2 √ cπn and that the distribution of the length is tightly concentrate...
متن کاملOn Increasing Subsequences Of
We study the fluctuations, in the large deviations regime, of the longest increasing subsequence of a random i.i.d. sample on the unit square. In particular, our results yield the precise upper and lower exponential tails for the length of the longest increasing subsequence of a random permutation. §.
متن کاملOn Increasing Subsequences of I.i.d. Samples
We study the uctuations, in the large deviations regime, of the longest increasing subsequence of a random i.i.d. sample on the unit square. In particular, our results yield the precise upper and lower exponential tails for the length of the longest increasing subsequence of a random permutation. i=1 denote a sequence of i.i.d. random variables with marginal law on the unit square Q = 0; 1] 2. ...
متن کاملOn the length of the longest monotone subsequence in a random permutation
In this short note we prove a concentration result for the length L n of the longest monotone increasing subsequence of a random permutation of the set but less is known about the concentration of L n around its mean. Our aim here is to prove the following.
متن کامل