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pro vyhledávání: '"Arratia, Richard"'
For a random binary noncoalescing feedback shift register of width $n$, with all $2^{2^{n-1}}$ possible feedback functions $f$ equally likely, the process of long cycle lengths, scaled by dividing by $N=2^n$, converges in distribution to the same Poi
Externí odkaz:
http://arxiv.org/abs/1903.09183
Autor:
Arratia, Richard, DeSalvo, Stephen
We consider uniformly random set partitions of size $n$ with exactly $k$ blocks, and uniformly random permutations of size $n$ with exactly $k$ cycles, under the regime where $n-k \sim t\sqrt{n}$, $t>0$. In this regime, there is a simple approximatio
Externí odkaz:
http://arxiv.org/abs/1807.03926
Autor:
Arratia, Richard
The scale invariant Poisson processes on (0,infty) play a central but mildly disguised role in number theory, combinatorics, and genetics. They give the continuous limits which underly and unify diverse discrete structures, including the prime factor
Externí odkaz:
http://arxiv.org/abs/1611.05572
Autor:
Arratia, Richard, DeSalvo, Stephen
We give a general framework for approximations to combinatorial assemblies, especially suitable to the situation where the number $k$ of components is specified, in addition to the overall size $n$. This involves a Poisson process, which, with the ap
Externí odkaz:
http://arxiv.org/abs/1606.04642
Asymptotics for Dickman's number theoretic function $\rho(u)$, as $u \rightarrow \infty$, were given de Bruijn and Alladi, and later in sharper form by Hildebrand and Tenenbaum. The perspective in these works is that of analytic number theory. Howeve
Externí odkaz:
http://arxiv.org/abs/1606.03524
Autor:
Arratia, Richard, Earnest, Michael
Motivated by the work of Fulman and Goldstein, comparing the distribution of the corank of random matrices in $\mathbb F_q[n]$ with the limit distribution as $n \to \infty$, we define a countdown process, driven by independent geometric random variab
Externí odkaz:
http://arxiv.org/abs/1605.04352
Publikováno v:
Bernoulli 24 (2018), 433-448
We remove the hypothesis "$S$ is finite" from the BKR inequality for product measures on $S^d$, which raises some issues related to descriptive set theory. We also discuss the extension of the BKR operator and inequality, from 2 events to 2 or more e
Externí odkaz:
http://arxiv.org/abs/1508.05337
Publikováno v:
Math. Mag. 88 (2015), 196-211
We look at the Florida Lottery records of winners of prizes worth $600 or more. Some individuals claimed large numbers of prizes. Were they lucky, or up to something? We distinguish the "plausibly lucky" from the "implausibly lucky" by solving optimi
Externí odkaz:
http://arxiv.org/abs/1503.02902
Autor:
Arratia, Richard, DeSalvo, Stephen
We provide completely effective error estimates for Stirling numbers of the first and second kind, denoted by $s(n,m)$ and $S(n,m)$, respectively. These bounds are useful for values of $m \geq n - O(\sqrt{n})$. An application of our Theorem 5 yields,
Externí odkaz:
http://arxiv.org/abs/1404.3007
Let $p_1 \ge p_2 \ge \dots$ be the prime factors of a random integer chosen uniformly from $1$ to $n$, and let $$ \frac{\log p_1}{\log n}, \frac{\log p_2}{\log n}, \dots $$ be the sequence of scaled log factors. Billingsley's Theorem (1972), in its m
Externí odkaz:
http://arxiv.org/abs/1401.1555