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Gelation for MarcusLushnikov Process
, 2010
"... MarcusLushnikov Process is a simple mean field model of coagulating particles that converges to the homogeneous Smoluchowski equation in the large mass limit. If the coagulation rates grow sufficiently fast as the size of particles get large, giant particles emerge in finite time. This is known as ..."
Abstract
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MarcusLushnikov Process is a simple mean field model of coagulating particles that converges to the homogeneous Smoluchowski equation in the large mass limit. If the coagulation rates grow sufficiently fast as the size of particles get large, giant particles emerge in finite time. This is known
Emergence of the Giant Component in Special MarcusLushnikov Processes
 Random Structures and Algorithms
, 1997
"... Component sizes in the usual random graph process are a special case of the MarcusLushnikov process discussed in the scientific literature, so it is natural to ask how theory surrounding emergence of the giant component generalizes to the MarcusLushnikov process. Essentially no rigorous results ar ..."
Abstract

Cited by 14 (4 self)
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9622859 MarcusLushnikov process. The model was introduced by Marcus [16], and further studied by Lush...
Merging costs for the additive MarcusLushnikov process, and UnionFind algorithms
"... Abstract. Starting with a monodisperse configuration with n size–1 particles, an additive Marcus–Lushnikov process evolves until it reaches its final state (a unique particle with mass n). At each of the n − 1 steps of its evolution, a merging cost is incurred, that depends on the sizes of the two p ..."
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Cited by 3 (0 self)
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Abstract. Starting with a monodisperse configuration with n size–1 particles, an additive Marcus–Lushnikov process evolves until it reaches its final state (a unique particle with mass n). At each of the n − 1 steps of its evolution, a merging cost is incurred, that depends on the sizes of the two
Deterministic and Stochastic Models for Coalescence (Aggregation, Coagulation): a Review of the MeanField Theory for Probabilists
 Bernoulli
, 1997
"... Consider N particles, which merge into clusters according to the rule: a cluster of size x and a cluster of size y merge at (stochastic) rate K(x; y)=N , where K is a specified rate kernel. This MarcusLushnikov model of stochastic coalescence, and the underlying deterministic approximation given by ..."
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Cited by 222 (13 self)
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Consider N particles, which merge into clusters according to the rule: a cluster of size x and a cluster of size y merge at (stochastic) rate K(x; y)=N , where K is a specified rate kernel. This MarcusLushnikov model of stochastic coalescence, and the underlying deterministic approximation given
A pure jump Markov process associated with Smoluchowski’s coagulation equation
 in "Ann. Probab.", 2002
"... The aim of the present paper is to construct a stochastic process, whose law is the solution of the Smoluchowski’s coagulation equation. We introduce first a modified equation, dealing with the evolution of the distribution Qt (dx) of the mass in the system. The advantage we take on this is that we ..."
Abstract

Cited by 9 (2 self)
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on this is that we can perform an unified study for both continuous and discrete models. The integropartialdifferential equation satisfied by {Qt}t≥0 can be interpreted as the evolution equation of the time marginals of a Markov pure jump process. At this end we introduce a nonlinear Poisson driven stochastic
Coupling algorithms for calculating sensitivities of Smoluchowski’s Coagulation equation
, 2009
"... In this paper, two new stochastic algorithms for calculating parametric derivatives of the solution to the Smoluchowski coagulation equation are presented. It is assumed that the coagulation kernel is dependent on these parameters. The new algorithms (called ‘Single ’ and ‘Double’) work by coupling ..."
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by coupling two MarcusLushnikov processes in such a way as to reduce the difference between their trajectories, thereby significantly reducing the variance of central difference estimators of the parametric derivatives. In the numerical results, the algorithms are shown have have a O(1/N) order
Results 1  10
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