Phase transition of the contact process on random regular graphs
نویسندگان
چکیده
منابع مشابه
A first order phase transition in the threshold θ ≥ 2 contact process on random r-regular graphs and r-trees
We consider the discrete time threshold-θ contact process on a random r-regular graph. We show that if θ ≥ 2, r ≥ θ + 2, 1 is small and p ≥ p1( 1), then starting from all vertices occupied the fraction of occupied vertices is ≥ 1 − 2 1 up to time exp(γ1(r)n) with high probability. We also show that for p2 < 1 there is an 2(p2) > 0 so that if p ≤ p2 and the initial density is ≤ 2(p2)n, then the ...
متن کاملContact Processes on Random Regular Graphs
We show that the contact process on a random d-regular graph initiated by a single infected vertex obeys the “cutoff phenomenon” in its supercritical phase. In particular, we prove that, when the infection rate is larger than the lower critical value of the contact process on the infinite d-regular tree, there are positive constants C, p depending on the infection rate such that for any ε > 0, ...
متن کاملContact Processes on Random Regular Graphs by Steven Lalley
We show that the contact process on a random d-regular graph initiated by a single infected vertex obeys the “cutoff phenomenon” in its supercritical phase. In particular, we prove that, when the infection rate is larger than the lower critical value of the contact process on the infinite d-regular tree, there are positive constants C, p depending on the infection rate such that for any ε > 0, ...
متن کاملOn the asymmetry of random regular graphs and random graphs
This paper studies the symmetry of random regular graphs and random graphs. Our main result shows that for all 3 ≤ d ≤ n − 4 the random d-regular graph on n vertices almost surely has no non-trivial automorphisms. This answers an open question of N. Wormald [13].
متن کاملThe phase transition in inhomogeneous random graphs
The ‘classical’ random graph models, in particular G(n, p), are ‘homogeneous’, in the sense that the degrees (for example) tend to be concentrated around a typical value. Many graphs arising in the real world do not have this property, having, for example, power-law degree distributions. Thus there has been a lot of recent interest in defining and studying ‘inhomogeneous’ random graph models. O...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2016
ISSN: 1083-6489
DOI: 10.1214/16-ejp4476