相关论文: Proof of Razumov-Stroganov conjecture for some inf…

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)…

In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.

We study quasi-stationary distributions and quasi-limiting behavior of Markov chains in general reducible state spaces with absorption. We propose a set of assumptions dealing with particular situations where the state space can be…

We define oriented posets with correpsonding rank matrices, where linking two posets by an edge corresponds to matrix multiplication. In particular, linking chains via this method gives us fence posets, and taking traces gives us circular…

We settle the Polynomial Freiman--Ruzsa (PFR/Marton) conjecture for the integers and for cyclic groups. More precisely, we show that if $A$ is a finite subset of $\mathbb{Z}$ or $\mathbb{Z}/N\mathbb{Z}$ with $|A+A| \le K|A|$, then there is…

The theorem of Lieb, Schultz and Mattis (LSM), which states that the S=1/2 XXZ spin chain has gapless or degenerate ground states, can be applied to broader models. Independently, Kolb considered the relation between the wave number $q$ and…

In this paper, we systematically study generalized Markov numbers arising from semigroups of reduced integer matrices. This construction allows us to find these numbers by counting perfect matchings of a new family of bipartite graphs,…

We show that a uniform probability measure supported on a specific set of piecewise linear loops in a non-trivial free homotopy class in a multi-punctured plane is overwhelmingly concentrated around loops of minimal lengths. Our approach is…

We prove stochastic stability of chaotic maps for a general class of Markov random perturbations (including singular ones) satisfying some kind of mixing conditions. One of the consequences of this statement is the proof of Ulam's…

Menon's proof of the preservation of log-concavity of sequences under convolution becomes simpler when adapted to 2-sided infinite sequences. Under assumption of log-concavity of two 2-sided infinite sequences, the existence of the…

We consider the Pfaffian-Grassmannian equivalence from the motivic point of view. The main result is that under certain numerical conditions, both sides of the equivalence are related on the level of Chow motives. The consequences include a…

Verification of infinite-state Markov chains is still a challenge despite several fruitful numerical or statistical approaches. For decisive Markov chains, there is a simple numerical algorithm that frames the reachability probability as…

The union-closed sets conjecture (Frankl's conjecture) says that for any finite union-closed family of finite sets, other than the family consisting only of the empty set, there exists an element that belongs to at least half of the sets in…

We exhibit an explicit sufficient condition for the Lyapunov exponents of a linear cocycle over a Markov map to have multiplicity 1. This builds on work of Guivarc'h-Raugi and Gol'dsheid-Margulis, who considered products of random matrices,…

We prove that the Khovanov homology of alternating knots and 2-component links is equal (as a singly graded group) to the singular homology of a certain space of trace- free, binary dihedral representations of the link group. More…

In [Pal13] (arXiv:1106.4540) the second author proved that the sequence of "oriented" configuration spaces on an open connected manifold exhibits homological stability as the number of particles goes to infinity. To complement that result…

We consider $m$-divisible non-crossing partitions of $\{1,2,\ldots,mn\}$ with the property that for some $t\leq n$ no block contains more than one of the first $t$ integers. We give a closed formula for the number of multi-chains of such…

We consider Markov chain Monte Carlo methods for calculating conditional p values of statistical models for count data arising in Box-Behnken designs. The statistical model we consider is a discrete version of the first-order model in the…

The notion of free link is a generalized notion of virtual link. In the present paper we define the group of free braids, prove the Alexander theorem that all free links can be obtained as closures of free braids and prove a Markov theorem,…

If the state space of a homogeneous continuous-time Markov chain is too large, making inferences - here limited to determining marginal or limit expectations - becomes computationally infeasible. Fortunately, the state space of such a chain…