اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدCoexistence of grass, saplings and trees in the Staver-Levin forest model
283
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this paper, we consider two attractive stochastic spatial models in which each site can be in state 0, 1 or 2: Krones model in which 0${}={}$vacant, 1${}={}$juvenile and 2${}={}$a mature individual capable of giving birth, and the Staver-Levin forest model in which 0${}={}$grass, 1${}={}$sapling and 2${}={}$tree. Our first result shows that if $(0,0)$ is an unstable fixed point of the mean-field ODE for densities of 1s and 2s then when the range of interaction is large, there is positive probability of survival starting from a finite set and a stationary distribution in which all three types are present. The result we obtain in this way is asymptotically sharp for Krones model. However, in the Staver-Levin forest model, if $(0,0)$ is attracting then there may also be another stable fixed point for the ODE, and in some of these cases there is a nontrivial stationary distribution.
قيم البحث
اقرأ أيضاً
Using a description of the Levin-Wen model excitations in terms of Wilson lines, we compute the degeneracy of the energy levels for any input anyon theory and for any trivalent graph embedded on any (orientable) compact surface. This result allows on
e to obtain the finite-size and finite-temperature partition function and to show that there are no thermal phase transitions.
We provide a uniform upper bound on the minimal drift so that the one-per-site frog model on a $d$-ary tree is recurrent. To do this, we introduce a subprocess that couples across trees with different degrees. Finding couplings for frog models on nes
ted sequences of graphs is known to be difficult. The upper bound comes from combining the coupling with a new, simpler proof that the frog model on a binary tree is recurrent when the drift is sufficiently strong. Additionally, we describe a coupling between frog models on trees for which the degree of the smaller tree divides that of the larger one. This implies that the critical drift has a limit as $d$ tends to infinity along certain subsequences.
The frog model is an infection process in which dormant particles begin moving and infecting others once they become infected. We show that on the rooted $d$-ary tree with particle density $Omega(d^2)$, the set of visited sites contains a linearly ex
panding ball and the number of visits to the root grows linearly with high probability.
The frog model is a branching random walk on a graph in which particles branch only at unvisited sites. Consider an initial particle density of $mu$ on the full $d$-ary tree of height $n$. If $mu= Omega( d^2)$, all of the vertices are visited in time
$Theta(nlog n)$ with high probability. Conversely, if $mu = O(d)$ the cover time is $exp(Theta(sqrt n))$ with high probability.
In work with a variety of co-authors, Staver and Levin have argued that savannah and forest coexist as alternative stable states with discontinuous changes in density of trees at the boundary. Here we formulate a nonhomogeneous spatial model of the c
ompetition between forest and savannah. We prove that coexistence occurs for a time that is exponential in the size of the system, and that after an initial transient, boundaries between the alternative equilibria remain stable.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
