Related papers: Markov's Theorem
In the first part of this paper we present a theory of proof nets for full multiplicative linear logic, including the two units. It naturally extends the well-known theory of unit-free multiplicative proof nets. A linking is no longer a set…
We give a survey of recent results, due mainly to the authors, concerning Bernstein-Markov type inequalities and connections with potential theory.
This is a review of current research in Markov chains as toric statistical models. Its content is mixture of background information, results from the relevant recent literature, new results, and work in progress.
Markov processes are popular mathematical models, studied by theoreticians for their intriguing properties, and applied by practitioners for their flexible structure. With this book we teach how to model and analyze Markov processes. We…
In order to obtain a Markov theorem without stabilization, Birman and Menasco introduced the notion of exchange related braids. In this paper I study the way the Fiedler polynomial distinguishes conjugacy classes of some particular braided…
Solutions to the Markov equation appear in many mathematical contexts. We aim to build on the understanding of them by proving a recent conjecture about Markov polynomials; solutions to a generalised version of the Markov equation. The…
A new object of the probability theory, two-sided chain of events (symbols), is introduced. A theory of multi-steps Markov chains with long-range memory, proposed earlier in Phys. Rev. E 68, 06117 (2003), is developed and used to establish…
We present and explore a general method for deriving a Lie-Markov model from a finite semigroup. If the degree of the semigroup is $k$, the resulting model is a continuous-time Markov chain on $k$ states and, as a consequence of the product…
Braid groups are an important and flexible tool used in several areas of science, such as Knot Theory (Alexander's theorem), Mathematical Physics (Yang-Baxter's equation) and Algebraic Geometry (monodromy invariants). In this note we will…
We study the graphs generated when the formula for linking Markov triples is applied to general triples of integers. We find there are a finite number of equivalence classes of graphs, each with particular properties.
By addressing a long-standing open problem, listed in a highly regarded collection of open questions in the field and described as a "worthwhile research project", this note extends Markov's theorem (Markoff, Math. Ann., 27:177-182, 1886)…
Gromov and Ivanov established an analogue of Leray's theorem on cohomology of contractible covers for bounded cohomology of amenable covers. We present an alternative proof of this fact, using classifying spaces of families of subgroups.
The notion of Vassiliev algebra in case of hanlebodies is developed. The analogues of the results of John Baez for links in handlebodies are proved. That means that there exists a one-to-one correspondence between the special class of…
We sharpen the bounds of J. Bourgain, A. Gamburd and P. Sarnak (2016) on the possible number of nodes outside the "giant component" and on the size of individual connected components in the suitably defined functional graph of Markoff…
We discuss the validity of the proof of the fixed numerator conjecture on Markov numbers, which is the main result of the paper mentioned in the title.
In this work, we find a closed form formula for the braid index of an $n$-bridge braid, a class of positive braid knots which simultaneously generalizes torus knots, 1-bridge braids, and twisted torus knots. Our proof is elementary,…
Dror Bar-Natan and Ofer Ron have questioned the accuracy of the statement on page 453, line 2 minus of my paper "Groups of Ribbon Knots", Topology Vol 37, No. 2, 441-458, that "It follows from the inductive proof that $\cal{R}_n$ is of…
This paper presents a novel theoretical Monte Carlo Markov chain procedure in the framework of graphs. It specifically deals with the construction of a Markov chain whose empirical distribution converges to a given reference one. The Markov…
This thesis develops and expands upon known techniques of mathematical physics relevant to the analysis of the popular Markov model of phylogenetic trees required in biology to reconstruct the evolutionary relationships of taxonomic units…
In this paper we prove the Gromov--Milman conjecture (the Dvoretzky type theorem) for homogeneous polynomials on $\mathbb R^n$, and improve bounds on the number $n(d,k)$ in the analogous conjecture for odd degrees $d$ (this case is known as…