Zobrazeno 1 - 10
of 46
pro vyhledávání: '"Yakubovich, Yuri"'
Autor:
Yakubovich, Yuri
Publikováno v:
Adv. Math., 457 (2024), 109908
We present an explicit construction of a Markovian random growth process on integer partitions such that given it visits some level $n$, it passes through any partition $\lambda$ of $n$ with equal probabilities. The construction has continuous time,
Externí odkaz:
http://arxiv.org/abs/2303.14472
Autor:
Yakubovich, Yuri
Publikováno v:
Statistics & Probability Letters, vol. 176, September 2021, 109136
We present a relatively simple and mostly elementary proof of the L\'evy--Khintchine formula for subordinators. The main idea is to study the Poisson process time-changed by the subordinator. The technical tools used are conditional expectations, pro
Externí odkaz:
http://arxiv.org/abs/2011.07324
Publikováno v:
Communications in Mathematical Physics (2019). https://doi.org/10.1007/s00220-019-03513-5
The class of minimal difference partitions MDP($q$) (with gap $q$) is defined by the condition that successive parts in an integer partition differ from one another by at least $q\ge 0$. In a recent series of papers by A. Comtet and collaborators, th
Externí odkaz:
http://arxiv.org/abs/1809.06122
Autor:
Pitman, Jim, Yakubovich, Yuri
Publikováno v:
Bernoulli 25, no. 4B (2019), 3623--3651
This article presents a limit theorem for the gaps $\widehat{G}_{i:n}:= X_{n-i+1:n} - X_{n-i:n}$ between order statistics $X_{1:n} \le \cdots \le X_{n:n}$ of a sample of size $n$ from a random discrete distribution on the positive integers $(P_1, P_2
Externí odkaz:
http://arxiv.org/abs/1804.10248
Autor:
Pitman, Jim, Yakubovich, Yuri
We consider shifts $\Pi_{n,m}$ of a partially exchangeable random partition $\Pi_\infty$ of $\mathbb{N}$ obtained by restricting $\Pi_\infty$ to $\{n+1,n+2,\dots, n+m\}$ and then subtracting $n$ from each element to get a partition of $[m]:= \{1, \ld
Externí odkaz:
http://arxiv.org/abs/1707.00313
Autor:
Pitman, Jim, Yakubovich, Yuri
We describe the distribution of frequencies ordered by sample values in a random sample of size $n$ from the two parameter GEM$(\alpha,\theta)$ random discrete distribution on the positive integers. These frequencies are a $($size$-\alpha)$-biased ra
Externí odkaz:
http://arxiv.org/abs/1704.04732
Autor:
Pitman, Jim, Yakubovich, Yuri
We show that in a sample of size $n$ from a GEM$(0,\theta)$ random discrete distribution, the gaps $G_{i:n}:= X_{n-i+1:n} - X_{n-i:n}$ between order statistics $X_{1:n} \le \cdots \le X_{n:n}$ of the sample, with the convention $G_{n:n} := X_{1:n} -
Externí odkaz:
http://arxiv.org/abs/1701.06294
Autor:
Pitman, Jim, Yakubovich, Yuri
We show that the maximal value in a size $n$ sample from GEM$(\theta)$ distribution is distributed as a sum of independent geometric random variables. This implies that the maximal value grows as $\theta\log(n)$ as $n\to\infty$. For the two-parametri
Externí odkaz:
http://arxiv.org/abs/1609.01601
Autor:
Krachun, Dmitry, Yakubovich, Yuri
The lattice of the set partitions of $[n]$ ordered by refinement is studied. Given a map $\phi: [n] \rightarrow [n]$, by taking preimages of elements we construct a partition of $[n]$. Suppose $t$ partitions $p_1,p_2,\dots,p_t$ are chosen independent
Externí odkaz:
http://arxiv.org/abs/1602.01270