排序方式: 共有12条查询结果,搜索用时 78 毫秒
1.
I. Kurkova 《Journal of statistical physics》2003,111(1-2):35-56
We consider the problem of temperature dependence of the Gibbs states in two spin-glass models: Derrida's Random Energy Model and its analogue, where the random variables in the Hamiltonian are replaced by independent standard Brownian motions. For both of them we compute in the thermodynamic limit the overlap distribution
N
i=1
i
i
/N[–1,1] of two spin configurations , under the product of two Gibbs measures, which are taken at temperatures T,T respectively. If TT are fixed, then at low temperature phase the results are different for these models: for the first one this distribution is D
0
0+D
1
1, with random weights D
0, D
1, while for the second one it is
0. We compute consequently the overlap distribution for the second model whenever T–T0 at different speeds as N. 相似文献
2.
A load-balanced network with two queues Q
1 and Q
2 is considered. Each queue receives a Poisson stream of customers at rate
i
, i=1,2. In addition, a Poisson stream of rate arrives to the system; the customers from this stream join the shorter of two queues. After being served in the ith queue, i=1,2, customers leave the system with probability 1–p
i
*, join the jth queue with probability p(i,j), j=1,2, and choose the shortest of two queues with probability p(i,{1,2}). We establish necessary and sufficient conditions for stability of the system. 相似文献
3.
Recently, Bauke and Mertens conjectured that the local statistics of energies in random spin systems with discrete spin space
should in most circumstances be the same as in the random energy model. We review some rigorous results confirming the validity
of this conjecture. In the context of the SK models, we analyse the limits of the validity of the conjecture for energy levels
growing with the volume of the system. In the case of the Generalised Random energy model, we give a complete analysis for
the behaviour of the local energy statistics at all energy scales. In particular, we show that, in this case, the REM conjecture
holds exactly up to energies E
N
< β
c
N, where β
c
is the critical temperature. We also explain the more complex behaviour that sets in at higher energies.
Research supported in part by the DFG in the Dutch-German Bilateral Research Group “Mathematics of Random Spatial Models from
Physics and Biology” and by the European Science Foundation in the Programme RDSES. 相似文献
4.
The randomized k‐number partitioning problem is the task to distribute N i.i.d. random variables into k groups in such a way that the sums of the variables in each group are as similar as possible. The restricted k‐partitioning problem refers to the case where the number of elements in each group is fixed to N/k. In the case k = 2 it has been shown that the properly rescaled differences of the two sums in the close to optimal partitions converge to a Poisson point process, as if they were independent random variables. We generalize this result to the case k > 2 in the restricted problem and show that the vector of differences between the k sums converges to a k ‐ 1‐dimensional Poisson point process. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007 相似文献
5.
6.
7.
Recently, Bauke and Mertens conjectured that the local statistics of energies in random spin systems with discrete spin space
should, in most circumstances, be the same as in the random energy model. Here we give necessary conditions for this hypothesis
to be true, which we show to be satisfied in wide classes of examples: short range spin glasses and mean field spin glasses
of the SK type. We also show that, under certain conditions, the conjecture holds even if energy levels that grow moderately
with the volume of the system are considered.
Research supported in part by the DFG in the Dutch-German Bilateral Research Group ``Mathematics of Random Spatial Models
from Physics and Biology' and by the European Science Foundation in the Programme RDSES. 相似文献
8.
9.
10.
A random walk in $\mathbf{Z}_+^2$ spatially homogeneous in the interior, absorbed at the axes, starting from an arbitrary point $(i_0,j_0)$ and with step probabilities drawn on Fig. 1 is considered. The trivariate generating function of probabilities that the random walk hits a given point $(i,j) \in \mathbf{Z}_+^2 $ at a given time $k\ge 0$ is made explicit. Probabilities of absorption at a given time $k$ and at a given axis are found, and their precise asymptotic is derived as the time $k\rightarrow \infty $ . The equivalence of two typical ways of conditioning this random walk to never reach the axes is established. The results are also applied to the analysis of the voter model with two candidates and initially, in the population $\mathbf{Z}$ , four connected blocks of same opinions. Then, a citizen changes his mind at a rate proportional to the number of his neighbors that disagree with him. Namely, the passage from four to two blocks of opinions is studied. 相似文献