Lang, Reinhard; Nguyen Xuan Xanh Smoluchowski’s theory of coagulation in colloids holds rigorously in the Boltzmann-Grad-limit. (English) Zbl 0449.60074 Z. Wahrscheinlichkeitstheor. Verw. Geb. 54, 227-280 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 36 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory Keywords:coalescing Brownian particles; Boltzman-Grad-limit; kinetic equations; propagation of chaos PDFBibTeX XMLCite \textit{R. Lang} and \textit{Nguyen Xuan Xanh}, Z. Wahrscheinlichkeitstheor. Verw. Geb. 54, 227--280 (1980; Zbl 0449.60074) Full Text: DOI References: [1] Berresford, G. C., A class of Nonlinear Partial Differential Equations and the Associated Markov Process, Z. Wahrscheinlichkeitstheorie Verw. Gebiete, 33, 237-251 (197576) · Zbl 0307.60068 [2] Bramson, M., Griffeath, D.: Clustering and Dispersion Rates for Some Interacting Particle Systems on ℤ. Preprint 1978 · Zbl 0429.60098 [3] Bramson, M., Griffeath, D.: Asymptotics for Interacting Systems on ℤ^d. Preprint 1979 · Zbl 0417.60097 [4] Carslaw, H. S.; Jaeger, J. C., Conduction of Heat in Solids (1959), Oxford: Clarendon Press, Oxford [5] Chandrasekhar, S., Stochastic Problems in Physics and Astronomy, Reviews of Modern Physics, 15, 1-89 (1943) · Zbl 0061.46403 [6] Itô, K.; McKean, H. P. Jr., Diffusion Processes and their Sample Paths (1974), New York: Springer, New York · Zbl 0285.60063 [7] Kac, M., Foundations of Kinetic Theory, Proc. Third Berkeley Sympos. Math. Statist. Probab., 3, 171-197 (1956) · Zbl 0072.42802 [8] Kac, M.; Cohen; Thirring, Some Probabilistic Aspects of the Boltzmann Equation, Acta Physica Austriaca, Suppl. X. The Boltzmann Equation. Theory and Applications, 397-400 (1973), Wien: Springer-Verlag, Wien [9] Kac, M., Probabilistic methods in some problems of scattering theory, Rocky Mountain J. Math., 4, 511-537 (1974) · Zbl 0314.47006 [10] Lanford, O. E. III; Moser, J., Time Evolution of Large Classical systems, Danamical Systems, Theory and Applications, 70-111 (1975), Berlin Heidelberg New York: Springer, Berlin Heidelberg New York [11] Lanford, O. E. III, On the derivation of the Boltzmann Equation, Astérisque, 40, 117-137 (1976) [12] Lanford, O.E. III: Lectures at the 3ième cycle. Lausanne (1978), unpublished [13] Lang, R., Nguyen Xuan Xanh: Smoluchowski’s Theory of Coagulation in Colloids holds rigorously in the Boltzmann-Grad-Limit. Proceedings of the International Colloquium on Random Fields, held in Esztergom, June 1979. To appear · Zbl 0486.60098 [14] McKean, H. P. Jr., Fluctuations in the kinetic theory of gases, Comm. Pure Appl. Math., 28, 435-455 (1975) [15] Neveu, J.; Hennequin, P. L., Processus Ponctuels, Ecole d’Eté de Probabilités de Saint-Flour VI (1977), Berlin Heidelberg New York: Springer, Berlin Heidelberg New York · Zbl 0439.60044 [16] Port, S. C.; Stone, Ch. J., Brownian Motion and Classical Potential Theory (1978), New York: Academic Press, New York · Zbl 0413.60067 [17] Rauch, J.; Taylor, M., Potential and Scattering Theory in Wildly Perturbed Domains, J. Funct. Anal., 18, 27-59 (1975) · Zbl 0293.35056 [18] Smoluchowski, M. v., Drei Vorträge über Diffusion, Brown’sche Molekularbewegung und Koagulation von Kolloidteilchen, Phys. Z., XVII, 557-571 (1916) [19] Smoluchowski, M. v., Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen, Z. physikalische Chemie, 92, 129-168 (1917) [20] Spitzer, F., Electrostatic Capacity, Heat Flow and Brownian Motion, Z. Wahrscheinlichkeitstheorie Verw. Gebiete, 3, 110-121 (1964) · Zbl 0126.33505 [21] Spohn, H.: Kinetic Equations from Hamiltonian Dynamics: The Markovian Limit. Lecture Notes, University of Leuven, 1979 · Zbl 0399.60082 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.