Feller property of the multiplicative coalescent with linear deletion
نویسنده
چکیده
We modify the definition of Aldous’ multiplicative coalescent process [3] and introduce the multiplicative coalescent with linear deletion (MCLD). A state of this process is a square-summable decreasing sequence of cluster sizes. Pairs of clusters merge with a rate equal to the product of their sizes and clusters are deleted with a rate linearly proportional to their size. We prove that the MCLD is a Feller process. This result is a key ingredient in the description of scaling limits of the evolution of component sizes of the mean field frozen percolation model [22] and the so-called rigid representation of such scaling limits [19].
منابع مشابه
On multiplicative (strong) linear preservers of majorizations
In this paper, we study some kinds of majorizations on $textbf{M}_{n}$ and their linear or strong linear preservers. Also, we find the structure of linear or strong linear preservers which are multiplicative, i.e. linear or strong linear preservers like $Phi $ with the property $Phi (AB)=Phi (A)Phi (B)$ for every $A,Bin textbf{M}_{n}$.
متن کاملBrownian Excursions, Critical Random Graphs and the Multiplicative Coalescent
Let (B t (s); 0 s < 1) be reeecting inhomogeneous Brownian motion with drift t ? s at time s, started with B t (0) = 0. Consider the random graph G(n; n ?1 +tn ?4=3), whose largest components have size of order n 2=3. Normalizing by n ?2=3 , the asymptotic joint distribution of component sizes is the same as the joint distribution of excursion lengths of B t (Corollary 2). The dynamics of mergi...
متن کاملAlmost n-Multiplicative Maps between Frechet Algebras
For the Fr'{e}chet algebras $(A, (p_k))$ and $(B, (q_k))$ and $n in mathbb{N}$, $ngeq 2$, a linear map $T:A rightarrow B$ is called textit{almost $n$-multiplicative}, with respect to $(p_k)$ and $(q_k)$, if there exists $varepsilongeq 0$ such that$$q_k(Ta_1a_2cdots a_n-Ta_1Ta_2cdots Ta_n)leq varepsilon p_k(a_1) p_k(a_2)cdots p_k(a_n),$$for each $kin mathbb{N}$ and $a_1, a_2, ldots, a_nin A$. Th...
متن کاملAlmost multiplicative linear functionals and approximate spectrum
We define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital Banach algebra A and show that the δ-approximate spectrum σ_δ (a) of a is compact. The relation between the δ-approximate spectrum and the usual spectrum is investigated. Also an analogue of the classical Gleason-Kahane-Zelazko theorem is established: For each ε>0, there is δ>0 such that if ϕ is...
متن کاملRESOLUTION METHOD FOR MIXED INTEGER LINEAR MULTIPLICATIVE-LINEAR BILEVEL PROBLEMS BASED ON DECOMPOSITION TECHNIQUE
In this paper, we propose an algorithm base on decomposition technique for solvingthe mixed integer linear multiplicative-linear bilevel problems. In actuality, this al-gorithm is an application of the algorithm given by G. K. Saharidis et al for casethat the rst level objective function is linear multiplicative. We use properties ofquasi-concave of bilevel programming problems and decompose th...
متن کامل