Zobrazeno 1 - 10
of 206
pro vyhledávání: '"Marynych, Alexander"'
For a right-continuous nondecreasing and unbounded function $V$ of at most exponential growth, which vanishes on the negative halfline, we investigate the asymptotic behavior of the Lebesgue-Stieltjes convolution powers $V^{\ast(j)}(t)$ as both $j$ a
Externí odkaz:
http://arxiv.org/abs/2404.04955
We introduce multinomial and $r$-variants of several classic objects of combinatorial probability, such as the random recursive and Hoppe trees, random set partitions and compositions, the Chinese restaurant process, Feller's coupling, and some other
Externí odkaz:
http://arxiv.org/abs/2403.16448
We study vantage-point trees constructed using an independent sample from the uniform distribution on a fixed convex body $K$ in $(\mathbb{R}^d,\|\cdot\|)$, where $\|\cdot\|$ is an arbitrary homogeneous norm on $\mathbb{R}^d$. We prove that a sequenc
Externí odkaz:
http://arxiv.org/abs/2312.05651
Autor:
Kabluchko, Zakhar, Marynych, Alexander
We study divisibility properties of a set $\{f_1(\mathbf{U}_n^{(s)}),\ldots,f_m(\mathbf{U}_n^{(s)})\}$, where $f_1,\ldots,f_m$ are polynomials in $s$ variables over $\mathbb{Z}$ and $\mathbf{U}_n^{(s)}$ is a point picked uniformly at random from the
Externí odkaz:
http://arxiv.org/abs/2311.05369
Let $(\xi_1, \eta_1)$, $(\xi_2, \eta_2),\ldots$ be independent identically distributed $\mathbb{N}^2$-valued random vectors with arbitrarily dependent components. The sequence $(\Theta_k)_{k\in\mathbb{N}}$ defined by $\Theta_k=\Pi_{k-1}\cdot\eta_k$,
Externí odkaz:
http://arxiv.org/abs/2310.05283
We consider the classic infinite occupancy scheme, where balls are thrown in boxes independently, with probability $p_j$ of hitting box $j$. Each time a box receives its first ball we speak of a record and, more generally, call an $r$-record every ev
Externí odkaz:
http://arxiv.org/abs/2308.01739
We investigate increasing propagation of chaos for the mean-field Ising model of ferromagnetism (also known as the Curie-Weiss model) with $N$ spins at inverse temperature $\beta>0$ and subject to an external magnetic field of strength $h\in\mathbb{R
Externí odkaz:
http://arxiv.org/abs/2307.05335
We introduce a branching process in a sparse random environment as an intermediate model between a Galton--Watson process and a branching process in a random environment. In the critical case we investigate the survival probability and prove Yaglom-t
Externí odkaz:
http://arxiv.org/abs/2306.06730
A crinkled subordinator is an $\ell^2$-valued random process which can be thought of as a version of the usual one-dimensional subordinator with each out of countably many jumps being in a direction orthogonal to the directions of all other jumps. We
Externí odkaz:
http://arxiv.org/abs/2306.04747
Autor:
Kabluchko, Zakhar, Marynych, Alexander
We prove limit theorems for random walks with $n$ steps in the $d$-dimensional Euclidean space as both $n$ and $d$ tend to infinity. One of our results states that the path of such a random walk, viewed as a compact subset of the infinite-dimensional
Externí odkaz:
http://arxiv.org/abs/2211.08538