Related papers: Spectral Monotonicity under Leaf Attachment and Li…

Let $\omega\subset\mathbb{R}^n$ be a bounded domain with Lipschitz boundary. For $\varepsilon>0$ and $n\in\mathbb{N}$ consider the infinite cone $\Omega_{\varepsilon}:=\big\{(x_1,x')\in (0,\infty)\times\mathbb{R}^n: x'\in\varepsilon…

We investigate the limiting behavior of random tree growth in preferential attachment models. The tree stems from a root, and we add vertices to the system one-by-one at random, according to a rule which depends on the degree distribution…

This paper studies the asymptotic spectral properties of the sample covariance matrix for high dimensional compositional data, including the limiting spectral distribution, the limit of extreme eigenvalues, and the central limit theorem for…

Eigenfunctions expansion for discrete symplectic systems on a finite discrete interval is established in the case of a general linear dependence on the spectral parameter as a significant generalization of the Expansion theorem given by…

Consider the normalized adjacency matrices of random $d$-regular graphs on $N$ vertices with fixed degree $d\geq 3$, and denote the eigenvalues as $\lambda_1=d/\sqrt{d-1}\geq \lambda_2\geq\lambda_3\cdots\geq \lambda_N$. We prove that the…

The article considers an inhomogeneous Erd\H{o}s-R\"enyi random graph on $\{1,\ldots, N\}$, where an edge is placed between vertices $i$ and $j$ with probability $\varepsilon_N f(i/N,j/N)$, for $i\le j$, the choice being made independent…

We present a novel way in which effective field theory (EFT) can break down in cosmological string backgrounds depending on the behavior of the quantum gravity cutoff in infinite distance limits, known as the species scale $\Lambda_s$.…

A vertex set $S$ is a generalized $k$-independent set if the induced subgraph $G[S]$ contains no tree on $k$ vertices. The generalized $k$-independence number $\alpha_k(G)$ is the maximum size of such a set. For a tree $T$ with $n$…

In 2021 Baudier, Motakis, Schlumprecht, and Zs\'ak proved that if a sequence of graphs $(G_k)_{k\in{\mathbb{N}}}$ contains the sequence of complete graphs with uniformly bounded distortion, then the sequence of lamplighter graphs on $G_k$'s…

Asymptotic (late-time) cosmology depends on the asymptotic (infinite-distance) limits of scalar field space in string theory. Such limits feature an exponentially decaying potential $V \sim \exp(- c \phi)$ with corresponding Hubble scale $H…

Let $\tau(G)$ and $\kappa'(G)$ denote the edge-connectivity and the spanning tree packing number of a graph $G$, respectively. Proving a conjecture initiated by Cioaba and Wong, Liu et al. in 2014 showed that for any simple graph $G$ with…

We study vectors chosen at random from a compact convex polytope in $\mathbb{R}^n$ given by a finite number of linear constraints. We determine which projections of these random vectors are asymptotically normal as $n\to\infty$. Marginal…

This is a revised version of our short note [arxiv.math.DG/0403065] where we discuss the monotonicity of the eigen-values of the Laplacian operator to the Ricci-Hamilton flow on a compact or a complete non-compact Riemannian manifold. We…

We introduce a model of evolving preferential attachment trees where vertices are assigned weights, and the evolution of a vertex depends not only on its own weight, but also on the weights of its neighbours. We study the distribution of…

We consider sparse inhomogeneous Erd\H{o}s-R\'enyi random graph ensembles where edges are connected independently with probability $p_{ij}$. We assume that $p_{ij}= \varepsilon_N f(w_i, w_j)$ where $(w_i)_{i\ge 1}$ is a sequence of…

For the random eigenvalues with density corresponding to the Jacobi ensemble $$c \cdot \prod_{i < j} | \lambda_i - \lambda_j |^\beta \prod^n_{i=1} (2 - \lambda_i)^a (2 + \lambda_i)^b I_{(-2,2)} (\lambda_i) $$ $(a, b > -1, \beta > 0) $ a…

In this note we consider SDEs of the type $\mathrm{d} X_t=[F (X_t) -A X_t] \mathrm{d} t +D \mathrm{d} W_t$ under the assumptions that $A$'s eigenvalues are all of positive real parts and $F (\cdot)$ has slower-than-linear growth rate. It is…

We analyse the ground state of spinless fermions on a lattice in a weakly disordered potential, interacting via a nearest neighbour interaction, by applying the self-consistent Hartree-Fock approximation. We find that charge density…

We present a class of static, spherically symmetric, non-singular solutions of the tree-level string effective action, truncated to first order in $\alpha'$. In the string frame the solutions approach asymptotically (at $r\to 0$ and $r\to…

We propose the following conjecture: For every fixed $\alpha\in [0,\frac 13)$, each graph of minimum degree at least $(1+\alpha)\frac k2$ and maximum degree at least $2(1-\alpha)k$ contains each tree with $k$ edges as a subgraph. Our main…