Related papers: The combinatorics of biased riffle shuffles
Mahlmann and Schindelhauer (2005) defined a Markov chain which they called $k$-Flipper, and showed that it is irreducible on the set of all connected regular graphs of a given degree (at least 3). We study the 1-Flipper chain, which we call…
Using the recently developed notion of permutation limits this paper derives the limiting distribution of the number of fixed points and cycle structure for any convergent sequence of random permutations, under mild regularity conditions.…
Denoising diffusion models have driven significant progress in the field of Bayesian inverse problems. Recent approaches use pre-trained diffusion models as priors to solve a wide range of such problems, only leveraging inference-time…
In the model of randomly perturbed graphs we consider the union of a deterministic graph $\mathcal{G}_\alpha$ with minimum degree $\alpha n$ and the binomial random graph $\mathbb{G}(n,p)$. This model was introduced by Bohman, Frieze, and…
Following Barany et al., who proved that large random lattice zonotopes converge to a deterministic shape in any dimension after rescaling, we establish a central limit theorem for finite-dimensional marginals of the boundary of the…
We consider the moduli space of bordered Riemann surfaces with boundary and marked points. Such spaces appear in open-closed string theory, particularly with respect to holomorphic curves with Lagrangian submanifolds. We consider a…
Define a permutation to be any sequence of distinct positive integers. Given two permutations p and s on disjoint underlying sets, we denote by p sh s the set of shuffles of p and s (the set of all permutations obtained by interleaving the…
In this paper, we study some cards shuffles which are used by magicians. We focus ourselves on the possibility to hit eventually the initial state after several shuffles. This is a classical problem arising in discrete dynamical systems.…
We define and study slider-pinning rigidity, giving a complete combinatorial characterization. This is done via direction-slider networks, which are a generalization of Whiteley's direction networks.
An experimental study of a granular surface submitted to a circular fluid motion is presented. The appearance of an instability along the sand-water interface is observed beyond a critical radius $r_c$. This creates ripples with a spiral…
In this paper, the problem of reconstruction of signals in mixed Lebesgue spaces from their random average samples has been studied. Probabilistic sampling inequalities for certain subsets of shift-invariant spaces have been derived. It is…
We review the possibility to use the renormalons emerging in the perturbation series of the twist-2 part of the nonsinglet structure functions FL, F2, F3, and g1 to make approximate predictions for the magnitude of the appertaining twist-4…
This paper is concerned with a rate-distortion theory for sequences of i.i.d. random variables with general distribution supported on general sets including manifolds and fractal sets. Manifold structures are prevalent in data science,…
In this paper, we introduce the notion of a bimodule with a factorization structure (BFS) and show that such a structure gives rise to an algebra morphism. We then prove that this framework offers an interpretation of the geometric…
We consider the problem of constructing explicit Hitting sets for Combinatorial Shapes, a class of statistical tests first studied by Gopalan, Meka, Reingold, and Zuckerman (STOC 2011). These generalize many well-studied classes of tests,…
We introduce the shuffle of deformed permutahedra (a.k.a. generalized permutahedra), a simple associative operation obtained as the Cartesian product followed by the Minkowski sum with the graphical zonotope of a complete bipartite graph.…
Twisted homomorphisms of bialgebras are bialgebra homomorphisms from the first into Drinfeld twistings of the second. They possess a composition operation extending composition of bialgebra homomorphisms. Gauge transformations of twists,…
A statistical analysis of the eigenfrequencies of two sets of superconducting microwave billiards, one with mushroom-like shape and the other from the familiy of the Limacon billiards, is presented. These billiards have mixed…
This article is an expository account of the theory of twisted commutative algebras, which simply put, can be thought of as a theory for handling commutative algebras with large groups of linear symmetries. Examples include the coordinate…
The knot invariant Upsilon, defined by Ozsvath, Stipsicz, and Szabo, induces a homomorphism from the smooth knot concordance group to the group of piecewise linear functions on the interval [0,2]. Here we define a set of related secondary…