Related papers: Limit theory for point processes in manifolds

In this note we consider the point process of eigenvalues of the tensor product of two independent random unitary matrices of size m by m and n by n. When n becomes large, the process behaves like the superposition of m independent sine…

Let $\eta_t$ be a Poisson point process with intensity measure $t\mu$, $t>0$, over a Borel space $\mathbb{X}$, where $\mu$ is a fixed measure. Another point process $\xi_t$ on the real line is constructed by applying a symmetric function…

We define the quantile set of order $\alpha \in \left[ 1/2,1\right) $ associated to a law $P$ on $\mathbb{R}^{d}$ to be the collection of its directional quantiles seen from an observer $O\in \mathbb{R}^{d}$. Under minimal assumptions these…

Motivated by Varadhan's theorem, we introduce Varadhan functions, variances, and means on compact Riemannian manifolds as smooth approximations to their Fr\'echet counterparts. Given independent and identically distributed samples, we prove…

The entropy accumulation theorem, and its subsequent generalized version, is a powerful tool in the security analysis of many device-dependent and device-independent cryptography protocols. However, it has the drawback that the finite-size…

We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…

We examine topological properties of pointed metric measure spaces $(Y, p)$ that can be realized as the pointed Gromov-Hausdorff limit of a sequence of complete, Riemannian manifolds $\{(M^n_i, p_i)\}_{i=1}^{\infty}$ with nonnegative Ricci…

We construct a flow of continuous time and discrete state branching processes. Some scaling limit theorems for the flow are proved, which lead to the path-valued branching processes and nonlocal branching superprocesses over the positive…

The random connection model is a random graph whose vertices are given by the points of a Poisson process and whose edges are obtained by randomly connecting pairs of Poisson points in a position dependent but independent way. We study…

Let $\mathbb{B}_p^N$ be the $N$-dimensional unit ball corresponding to the $\ell_p$-norm. For each $N\in\mathbb N$ we sample a uniform random subspace $E_N$ of fixed dimension $m\in\mathbb{N}$ and consider the volume of $\mathbb{B}_p^N$…

The paper deals with a random connection model, a random graph whose vertices are given by a homogeneous Poisson point process on $\mathbb{R}^d$, and edges are independently drawn with probability depending on the locations of the two end…

For a sequence of i.i.d. random variables $\{\xi_x : x\in \bb Z\}$ bounded above and below by strictly positive finite constants, consider the nearest-neighbor one-dimensional simple exclusion process in which a particle at $x$ (resp.…

We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dimensional collective variables given by the shares of each…

In this work we derive limit theorems for trawl processes. First,we study the asymptotic behaviour of the partial sums of the discretized trawl process $(X_{i\Delta_{n}})_{i=0}^{\lfloor nt\rfloor-1}$, under the assumption that as…

This paper considers the entropy of the sum of (possibly dependent and non-identically distributed) Bernoulli random variables. Upper bounds on the error that follows from an approximation of this entropy by the entropy of a Poisson random…

For a stationary sequence of random variables we derive a self-normalized functional limit theorem under joint regular variation with index $\alpha \in (0,2)$ and weak dependence conditions. The convergence takes place in the space of…

Let $\big(M_k, Q_k\big)_{k\in\mathbb{N}}$ be independent copies of an $\mathbb{R}^2$-valued random vector. It is known that if $Y_n:=Q_1+M_1Q_2+...+M_1\cdot...\cdot M_{n-1}Q_n$ converges a.s. to a random variable $Y$, then the law of $Y$…

Let $\{X, X_n, n\geq 1\}$ be a sequence of independent identically distributed non-degenerate random variables. Put $S_0=0, S_n = \sum^n_{i=1} X_i$ and $V_n^2=\sum^n_{i=1} X_i^2, n\ge 1.$ A weak convergence theorem is established for the…

We establish a functional limit law of the logarithm for the increments of the normed quantile process based upon a random sample of size $n\to\infty$. We extend a limit law obtained by Deheuvels and Mason (12), showing that their results…

We propose an aproach for asymptotic analysis of plane partition statistics related to counts of parts whose sizes exceed a certain suitably chosen level. In our study, we use the concept of conjugate trace of a plane partition of the…