Mixing time of the card-cyclic-to-random shuffle
نویسندگان
چکیده
منابع مشابه
Probabilistic and combinatorial aspects of the card-cyclic to random insertion shuffle
of the Card-Cyclic to Random Insertion Shuffle Ross Pinsky Technion Consider a permutation σ ∈ Sn as a deck of cards numbered from 1 to n and laid out in a row, where σj denotes the number of the card that is in the j-th position from the left. We study some probabilistic and combinatorial aspects of the shuffle on Sn defined by removing and then randomly reinserting each of the n cards once, w...
متن کاملMixing Time of the Rudvalis Shuffle
We extend a technique for lower-bounding the mixing time of card-shuffling Markov chains, and use it to bound the mixing time of the Rudvalis Markov chain, as well as two variants considered by Diaconis and Saloff-Coste. We show that in each case Θ(n log n) shuffles are required for the permutation to randomize, which matches (up to constants) previously known upper bounds. In contrast, for the...
متن کاملCard-cyclic-to-random shuffling with relabeling
The card-cyclic-to-random shuffle is the card shuffle where the n cards are labeled 1, . . . , n according to their starting positions. Then the cards are mixed by first picking card 1 from the deck and reinserting it at a uniformly random position, then repeating for card 2, then for card 3 and so on until all cards have been reinserted in this way. Then the procedure starts over again, by fir...
متن کاملImproved Mixing Time Bounds for the Thorp Shuffle
E. Thorp introduced the following card shuffling model. Suppose the number of cards n is even. Cut the deck into two equal piles. Drop the first card from the left pile or from the right pile according to the outcome of a fair coin flip. Then drop from the other pile. Continue this way until both piles are empty. We show that if n is a power of 2 then the mixing time of the Thorp shuffle is O(l...
متن کاملRandom Transposition Shuffle
Recall that variation distance is defined as ‖μ− ξ‖ = 12 ∑ x∈Ω |μ(x)− ξ(x)| = maxA⊂Ω |μ(A)− ξ(A)|. Recall also that for any t > τmix · dln −1e we have ∆(t) ≤ . In general, our goal was to randomly sample elements of a large set Ω from a distribution defined implicitly by assigning a positive weight w(x) to each x ∈ Ω and then normalizing. So, Pr[x is choosen] = w(x) Z where Z = ∑ x∈Ω w(x). Howe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2014
ISSN: 1050-5164
DOI: 10.1214/13-aap964