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pro vyhledávání: '"Granovsky, Boris"'
Autor:
Granovsky, Boris
It is derived the explicit asymptotic expression in $n$ for the coefficient $c_n$ of the generating function for multiplicative structures with sub exponential rate of growth of $c_n,$ as $n\to\infty$.
Externí odkaz:
http://arxiv.org/abs/1705.00438
Autor:
Granovsky, Boris
In this paper we prove the necessity of the main sufficient condition of Meinardus for sub exponential rate of growth of the number of structures, having multiplicative generating functions of a general form and establish a new necessary and suffcien
Externí odkaz:
http://arxiv.org/abs/1606.08016
Autor:
Granovsky, Boris L., Stark, Dudley
A theorem of Meinardus provides asymptotics of the number of weighted partitions under certain assumptions on associated ordinary and Dirichlet generating functions. The ordinary generating functions are closely related to Euler's generating function
Externí odkaz:
http://arxiv.org/abs/1311.2254
Autor:
Granovsky, Boris, Stark, Dudley
Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing \cite{GSE}, we derive asymptotics for the number
Externí odkaz:
http://arxiv.org/abs/1102.5608
We prove that time dynamics of a stochastic process of pure coagulation is given by a time dependent Gibbs distribution if and only if rates of single coagulations have the form $\psi(i,j)=if(j)+jf(i)$, where $f$ is an arbitrary nonnegative function
Externí odkaz:
http://arxiv.org/abs/1008.1027
We establish a characterization of coagulation-fragmentation processes, such that the induced birth and death processes depicting the total number of groups at time $t\ge 0$ are time homogeneous. Based on this, we provide a characterization of mean-f
Externí odkaz:
http://arxiv.org/abs/0711.0503
We give a probalistic proof of the famous Meinardus' asymptotic formula for the number of weighted partitions with weakened one of the three Meinardus' conditions, and extend the resulting version of the theorem to other two classis types of decompos
Externí odkaz:
http://arxiv.org/abs/math/0701584
Autor:
Granovsky, Boris L.
We establish necessary and sufficient conditions for convergence (in the sense of finite dimensional distributions) of multiplicative measures on the set of partitions. We show that this convergence is equivalent to asymptotic independence of finite
Externí odkaz:
http://arxiv.org/abs/math/0511381
Autor:
Erlihson, Michael, Granovsky, Boris
We find limit shapes for a family of multiplicative measures on the set of partitions, induced by exponential generating functions with expansive parameters, $a_k\sim Ck^{p-1}, k\to\infty, p>0$,where $C$ is a positive constant. The measures considere
Externí odkaz:
http://arxiv.org/abs/math/0507343
Autor:
Granovsky, Boris L., Stark, Dudley
Publikováno v:
Journal London Math. Soc. (2) 73 (2006) 252-272
Given a sequence of integers $a_j, j\ge 1,$ a multiset is a combinatorial object composed of unordered components, such that there are exactly $a_j$ one-component multisets of size $j.$ When $a_j\asymp j^{r-1} y^j$ for some $r>0$, $y\geq 1$, then the
Externí odkaz:
http://arxiv.org/abs/math/0407322