Related papers: Uniform measures on braid monoids and dual braid m…

For a finite Thurston type ordering < of the braid group B_{n}, we introduce a new normal form of a dual positive braid which we call the C-normal form. This normal form extends Fromentin's rotating normal form and the author's C-normal…

The existence of the weak limit as n --> infinity of the uniform measure on rooted triangulations of the sphere with n vertices is proved. Some properties of the limit are studied. In particular, the limit is a probability measure on random…

In this note we show that the support of a locally $k$-uniform measure in $\mathbb R^{n+1}$ satisfies a kind of unique continuation property. As a consequence, we show that locally uniformly distributed measures satisfy a weaker unique…

The paper is devoted to prove a version of Milnor-Moore Theorem for connected braided bialgebras that are infinitesimally cocommutative. Namely in characteristic different from 2, we prove that, for a given connected braided bialgebra $A$…

We study a class of bistochastic matrices generalizing unistochastic matrices. Given a complex bipartite unitary operator, we construct a bistochastic matrix having as entries the normalized squares of Frobenius norm of the blocks. We show…

We initiate a systematic investigation of group actions on compact medain algebras via the corresponding dynamics on their spaces of measures. We show that a probability measure which is invariant under a natural push forward operation must…

We study the Morton-Franks-Williams inequality for closures of simple braids (also known as positive permutation braids). This allows to prove, in a simple way, that the set of simple braids is a orthonormal basis for the inner product of…

Let \Lambda be a finite subset of Z^d. We study the following sandpile model on \Lambda. The height at any given vertex x of \Lambda is a positive real number, and additions are uniformly distributed on some interval [a,b], which is a…

We adopt an empirical approach to the characterization of the distribution of twin primes within the set of primes, rather than in the set of all natural numbers. The occurrences of twin primes in any finite sequence of primes are like…

We define a measure of "complexity" of a braid which is natural with respect to both an algebraic and a geometric point of view. Algebraically, we modify the standard notion of the length of a braid by introducing generators $\Delta\_{ij}$,…

Let C be a locally convex subset of a negatively curved Riemannian manifold M. We define the skinning measure on the outer unit normal bundle to C in M by pulling back the Patterson-Sullivan measures at infinity, and give a finiteness…

We examine Fourier frames and, more generally, frame measures for different probability measures. We prove that if a measure has an associated frame measure, then it must have a certain uniformity in the sense that the weight is distributed…

We describe the structure of the monoid of natural-valued monotone functions on an arbitrary poset. For this monoid we provide a presentation, a characterization of prime elements, and a description of its convex hull. We also study the…

We apply ideas from the theory of limits of dense combinatorial structures to study order types, which are combinatorial encodings of finite point sets. Using flag algebras we obtain new numerical results on the Erd\H{o}s problem of finding…

We study a skew product with a curve of neutral points. We show that there exists a unique absolutely continuous invariant probability measure, and that the Birkhoff averages of a sufficiently smooth observable converge to a normal law or a…

Benardete, Gutierrez and Nitecki showed an important result which relates the geometrical properties of a braid, as a homeomorphism of the punctured disk, to its algebraic Garside-theoretical properties. Namely, they showed that if a braid…

We give an algorithm to decide if a given braid is a product of two factors which are conjugates of given powers of standard generators of the braid group. The same problem is solved in a certain class of Garside groups including Artin-Tits…

We study the connections between three seemingly different combinatorial structures - "uniform" brackets in statistics and probability theory, "containers" in online and distributed learning theory, and "combinatorial Macbeath regions", or…

We characterise positive braid links with positive Seifert form via a finite number of forbidden minors. From this we deduce a one-to-one correspondence between prime positive braid links with positive Seifert form and simply laced Dynkin…

We examine measure preserving mappings $f$ acting from a probability space $(\Omega, F,\mu) $ into a probability space $% (\Omega ^{*},F^{*},\mu ^{*}) ,$ where $\mu ^{*}=\mu (f^{-1})$. Conditions on $f$, under which $f$ preserves the…