相关论文: Big Ramsey spectra of countable chains

We prove the Erd\H os--S\'os conjecture for trees with bounded maximum degree and large dense host graphs. As a corollary, we obtain an upper bound on the multicolour Ramsey number of large trees whose maximum degree is bounded by a…

We show that coalgebras whose lattice of right coideals is distributive are coproducts of coalgebras whose lattice of right coideals is a chain. Those chain coalgebras are characterized as finite duals of noetherian chain rings whose…

The idea of this paper is to explore the existence of canonical countably saturated models for different classes of structures. It is well-known that, under CH, there exists a unique countably saturated linear order of cardinality…

In this article we give an explicit classification for the countably infinite graphs $\mathcal{G}$ which are, for some $k$, $\geq$$ k$-homogeneous. It turns out that a $\geq$$k-$homogeneous graph $\mathcal{M}$ is non-homogeneous if and only…

The spectral statistics and entanglement within the eigenstates of generic spin chain Hamiltonians are analysed. A class of random matrix ensembles is defined which include the most general nearest-neighbour qubit chain Hamiltonians. For…

An ordered hypergraph is a hypergraph $H$ with a specified linear ordering of the vertices, and the appearance of an ordered hypergraph $G$ in $H$ must respect the specified order on $V(G)$. In on-line Ramsey theory, Builder iteratively…

The Carlson-Simpson lemma is a combinatorial statement occurring in the proof of the Dual Ramsey theorem. Formulated in terms of variable words, it informally asserts that given any finite coloring of the strings, there is an infinite…

By recent work of \citet{DobrinenICM} and \citet{Balko7} we know that every finite $G$ in the Henson graph $\mathbb{H}_{n+1}$ (the universal ultrahomogeneous $(n+1)$-clique free graph) has exact finite big Ramsey degree $k({G,n})$. That is,…

Ramsey theory looks for regularities in large objects. Model theory studies algebraic structures as models of theories. The structural Ramsey theory combines these two fields and is concerned with Ramsey-type questions about certain…

Assume hat a functionally Hausdorff space $X$ is a continuous image of a \v{C}ech complete space $P$ with Lindel\"of number $l(P)<\mathfrak c$. Then the following conditions are equivalent: (i) every compact subset of $X$ is scattered, (ii)…

We prove that the absolute spectral gap of any monotone Markov chain coincides with its optimal Ollivier-Ricci curvature, where the word `optimal' refers to the choice of the underlying metric. Moreover, we provide a new expression in terms…

The Scott rank of a countable structure is a measure, coming from the proof of Scott's isomorphism theorem, of the complexity of that structure. The Scott spectrum of a theory (by which we mean a sentence of $\mathcal{L}_{\omega_1 \omega}$)…

We prove deviation bounds for the random variable $\sum_{i=1}^{n} f_i(Y_i)$ in which $\{Y_i\}_{i=1}^{\infty}$ is a Markov chain with stationary distribution and state space $[N]$, and $f_i: [N] \rightarrow [-a_i, a_i]$. Our bound improves…

The infinite pigeonhole principle for $k$ colors ($\mathsf{RT}_k$) states, for every $k$-partition $A_0 \sqcup \dots \sqcup A_{k-1} = \mathbb{N}$, the existence of an infinite subset~$H \subseteq A_i$ for some~$i < k$. This seemingly…

Let $f$ be the $\mathbb{F}_q$-linear map over $\mathbb{F}_{q^{2n}}$ defined by $x\mapsto x+ax^{q^s}+bx^{q^{n+s}}$ with $\gcd(n,s)=1$. It is known that the kernel of $f$ has dimension at most $2$, as proved by Csajb\'ok et al. in "A new…

The eigenvalues of quantum chaotic systems have been conjectured to follow, in the large energy limit, the statistical distribution of eigenvalues of random ensembles of matrices of size $N\rightarrow\infty$. Here we provide semiclassical…

The paper investigates recoverability of discrete time signals represented by infinite sequences from incomplte observations. It is shown that there exist wide classes of signals that are everywhere dense in the space of square-summable…

A topological space is iso-dense if it has a dense set of isolated points. A topological space is scattered if each of its non-empty subspaces has an isolated point. In $\mathbf{ZF}$, in the absence of the axiom of choice, basic properties…

We show that Ramsey theory, a domain presently conceived to guarantee the existence of large homogeneous sets for partitions on k-tuples of words (for every natural number k) over a finite alphabet, can be extended to one for partitions on…

We investigate the spectral distribution of large sample covariance matrices with independent columns and entries in the columns that stem from Markov chains. We characterize the limiting spectral densities by their moments.…