Download Multitype Contact Process on Z: Extinction and Interface by Daniel R. Valesin PDF

By Daniel R. Valesin

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We omit its proof since it is simply a repetition of the above arguments. 6. Let H(−∞,0) = inf{n : X n < 0}. Then, sup x>0 x( |X H(−∞,0) |; H(−∞,0) < H0 ) ≤ sup x>0 x |X H(−∞,0) | < ∞. ; Pardoux, Etienne Survival of a single mutant in one dimension. Electron. J. Probab. 15 (2010), no. ; Mountford, Thomas; Pimentel, Leandro P. ; Valesin, Daniel Tightness for the interface of the one-dimensional contact process. Bernoulli 16, Number 4 (2010), 909-925. ; Sun, Rongfeng; Valle, G. Convergence results and sharp estimates for the voter model interfaces.

1. There exists C > 0 such that, for x ∈ , x (H 0 > N) < C|x| N . 1 will be carried out in a series of results. Fix L > 0 such that Ge−g L < 1 and let I = [−L, L]. Put εz = Ge−g|z| for z ∈ I c and εz = 1 for z ∈ I. 5) + (1 − εz )gz . 6) (Of course, if z ∈ I we must have bz1 = πz , bz2 = π). We will construct the process (X n ) coupled with other processes of interest. Let (X n , Zn ) be a Markov chain on × {0, 1} with transitions Q((x, i), ( y, j)) = ε x · b1x ( y − x) (1 − ε x ) · g x ( y − x) if j = 1; if j = 0.

ISBN: 0-534-09462-7 MR0940469 [7] Durrett, Rick Probability: theory and examples. Fourth edition. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge, 2010. x+428 pp. ISBN: 978-0-521-76539-8, 60-01 MR2722836 [8] Durrett, Rick; Swindle, Glen Are there bushes in a forest? Stochastic Process. Appl. 37 (1991), no. 1, 19-31 MR1091691 [9] Kuczek, Thomas The central limit theorem for the right edge of supercritical oriented percolation. Ann. Probab. 17 (1989), no.

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