Related papers: A generalization of carries process and riffle shu…
This paper concerns a probability distribution on the symmetric group generalizing the riffle shuffle of Bayer, Diaconis, and others. There are close connections with the theory of quasisymmetric and symmetric functions.
We study a generalization of Holte's amazing matrix, the transition probability matrix of the Markov chains of the 'carries' in a non-standard numeration system. The stationary distributions are explicitly described by the numbers which can…
We study the cutoff phenomenon for generalized riffle shuffles where, at each step, the deck of cards is cut into a random number of packs of multinomial sizes which are then riffled together.
In this paper we study random orderings of the integers with a certain invariance property. We describe all such orders in a simple way. We define and represent random shuffles of a countable set of labels and then give an interpretation of…
In this expository article, we highlight the direct connection between card shuffling and the functions known as $P$-partitions that come from algebraic combinatorics. While many (but not all) of the results we discuss are known, we give a…
We introduce a new type of card shuffle called one-sided transpositions. At each step a card is chosen uniformly from the pack and then transposed with another card chosen uniformly from below it. This defines a random walk on the symmetric…
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
We study a simple generalization of the rotation (or circular shift) of the binary sequences. In particular, we show each orbit of this generalized rotation has a certain statistical symmetry. This generalized rotation naturally arises when…
We consider a generalized riffle shuffle on the colored permutation group $G_{p, n}$ and derive a determinantal formula for the probability of finding descents at given positions, proof of which is based on the bijection between the set of…
The paper deals with three generalized dependent setups arising from a sequence of Bernoulli trials. Various distributional properties, such as probability generating function, probability mass function and moments are discussed for these…
This paper studies biased riffle shuffles, first defined by Diaconis, Fill, and Pitman. These shuffles generalize the well-studied Gilbert-Shannon-Reeds shuffle and convolve nicely. An upper bound is given for the time for these shuffles to…
In this article we present a unification of the theory of algebraic, singular, topological and directional transition matrices by introducing the (generalized) transition matrix which encompasses each of the previous four. Some transition…
We study different fractional extensions of the Poisson process and generalized counting processes by introducing time-change represented by the inverse to the sums of stable and tempered stable subordinators. We state the governing…
Type A affine shuffles are compared with riffle shuffles followed by a cut. Although these probability measures on the symmetric group S_n are different, they both satisfy a convolution property. Strong evidence is given that when the…
A Markov chain is considered whose states are orderings of an underlying fixed tree and whose transitions are local "random-to-front" reorderings, driven by a probability distribution on subsets of the leaves. The eigenvalues of the…
We find explicit eigenvectors for the transition matrix of a random walk due to Bidegare, Hanlon and Rockmore. This is accomplished by using Brown and Diaconis' analysis of its stationary distribution, together with some combinatorics of…
We consider a continuous-time random walk which is the generalization, by means of the introduction of waiting periods on sites, of the one-dimensional nonhomogeneous random walk with a position-dependent drift known in the mathematical…
This paper studies statistics of riffle shuffles by relating them to random word statistics with the use of inverse shuffles. Asymptotic normality of the number of descents and inversions in riffle shuffles with convergence rates of order…
The typicality approach and the Hilbert space averaging method as its technical manifestation are important concepts of quantum statistical mechanics. Extensively used for expectation values we extend them in this paper to transition…
The main message in this paper is that there are surprisingly many different Brownian bridges, some of them - familiar, some of them - less familiar. Many of these Brownian bridges are very close to Brownian motions. Somewhat loosely…