اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدFusion coefficients and random walks in alcoves
162
0
0.0
(
0
)
تأليف
Manon Defosseux
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We point out a connection between fusion coefficients and random walks in a fixed level alcove associated to the root system of an affine Lie algebra and use this connection to solve completely the Dirichlet problem on such an alcove for a large class of simple random walks. We establish a correspondence between the hypergroup of conjugacy classes of a compact Lie group and the fusion hypergroup. We prove that a random walk in an alcove, obtained with the help of fusion coefficients, converges, after a proper normalization, towards the radial part of a Brownian motion on a compact Lie group.
قيم البحث
اقرأ أيضاً
The reproduction speed of a continuous-time branching random walk is proportional to a positive parameter $lambda$. There is a threshold for $lambda$, which is called $lambda_w$, that separates almost sure global extinction from global survival. Anal
ogously, there exists another threshold $lambda_s$ below which any site is visited almost surely a finite number of times (i.e.~local extinction) while above it there is a positive probability of visiting every site infinitely many times. The local critical parameter $lambda_s$ is completely understood and can be computed as a function of the reproduction rates. On the other hand, only for some classes of branching random walks it is known that the global critical parameter $lambda_w$ is the inverse of a certain function of the reproduction rates, which we denote by $K_w$. We provide here new sufficient conditions which guarantee that the global critical parameter equals $1/K_w$. This result extends previously known results for branching random walks on multigraphs and general branching random walks. We show that these sufficient conditions are satisfied by periodic tree-like branching random walks. We also discuss the critical parameter and the critical behaviour of continuous-time branching processes in varying environment. So far, only examples where $lambda_w=1/K_w$ were known; here we provide an example where $lambda_w>1/K_w$.
Lecture Notes. Minicourse given at the workshop Activated Random Walks, DLA, and related topics at IMeRA-Marseille, March 2015.
We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. This model is known to exhibit a phase transition: If $d ge 3$ and the environment is not too random, then, the total population gro
ws as fast as its expectation with strictly positive probability. If,on the other hand, $d le 2$, or the environment is ``random enough, then the total population grows strictly slower than its expectation almost surely. We show the equivalence between the slow population growth and a natural localization property in terms of replica overlap. We also prove a certain stronger localization property, whenever the total population grows strictly slower than its expectation almost surely.
We study survival of nearest-neighbour branching random walks in random environment (BRWRE) on ${mathbb Z}$. A priori there are three different regimes of survival: global survival, local survival, and strong local survival. We show that local and st
rong local survival regimes coincide for BRWRE and that they can be characterized with the spectral radius of the first moment matrix of the process. These results are generalizations of the classification of BRWRE in recurrent and transient regimes. Our main result is a characterization of global survival that is given in terms of Lyapunov exponents of an infinite product of i.i.d. $2times 2$ random matrices.
The integer points (sites) of the real line are marked by the positions of a standard random walk. We say that the set of marked sites is weakly, moderately or strongly sparse depending on whether the jumps of the standard random walk are supported b
y a bounded set, have finite or infinite mean, respectively. Focussing on the case of strong sparsity we consider a nearest neighbor random walk on the set of integers having jumps $pm 1$ with probability $1/2$ at every nonmarked site, whereas a random drift is imposed at every marked site. We prove new distributional limit theorems for the so defined random walk in a strongly sparse random environment, thereby complementing results obtained recently in Buraczewski et al. (2018+) for the case of moderate sparsity and in Matzavinos et al. (2016) for the case of weak sparsity. While the random walk in a strongly sparse random environment exhibits either the diffusive scaling inherent to a simple symmetric random walk or a wide range of subdiffusive scalings, the corresponding limit distributions are non-stable.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
