Probab. Th. Rel. Fields 71,581-613 (1986) Probability Theory= - 9 Springer-Verlag 1986 A Propagation of Chaos Result for Burgers' Equation A.S. Sznitman Laboratoire de Probabilit6s, associ6 C.N.R.S. n ~ 224, Universit6 Paris VI, 4, place Jussieu, F-75005 Paris, France I. Introduction In [15], McKean posed the problem of constructing a system of N interacting particles in ~ with generator 102 1 (~x c~) L=~ ~ ~-~.~ ~ ~ ~(x~-x J) +~ . 9 ox i 2(N-1)~<j (1.1) He conjectured that when the initial conditions are independent and u 0 distrib- uted, and if one looks at the law at time t of the first k particles, k fixed, letting the number N of interacting particles be larger and larger, one restores asymp- X 1 k totically at time t the independence of our first k particles ( t .... ,Xt), and that their common limiting (N --, m), distribution is given by the value at time t of the solution of Burgers' equation: 0u 1 02u 0u at 2 0x 2 u ~xx' with initial condition u 0 at time 0. (1.2) Such a type of phenomenon is called propagation of chaos (see Kac [12]). Several results concerning the questions of propagation of chaos and Burgers' equation have already been obtained, in Calderoni-Pulvirenti [2], where a smoothing procedure of the a-function is used, in Gutkin-Kac [-6], and Kotani- Osada [13], where the approach for the construction of the N-particle process and for the propagation of chaos result is rather analytical. The approach presented here is probabilistic. We consider a system of N particles satisfying: dXi=dBi+ N ~ dL~ i-XJ), i= 1.... , N, (1.3) j#i x~ =x'(0), where L~ j) is the symmetric local time in 0 of X~-X J, B ~ are inde- pendent Brownian motions, independent of the initial conditions (X~(0)), with