Related papers: Random Energy Model with complex replica number, c…
The alternative replica technique which involve summation over all integer momenta of the partition function and which does not require analytic continuation to non-integer values of the replica parameter $n$ is discussed. In terms of this…
In a recent Physics Review Letter, Dorlas and Wedagedera have studied the random energy model with an additional p-spin ferromagnetic interaction. Here we note that (i) we have solved the corresponding problem of a spherical spin system…
The presence of unobserved node specific heterogeneity in Exponential Random Graph Models (ERGM) is a general concern, both with respect to model validity as well as estimation instability. We therefore extend the ERGM by including node…
A theoretical description for the radial density profile of a finite number of identical charged particles confined in a harmonic trap is developed for application over a wide range of Coulomb coupling (or, equivalently, temperatures) and…
Dynamical systems has a variety of applications for the new information generated during the time. Many phenomenons like physical, chemical or social are not static, then an analysis over the time is necessary. In this work, an experimental…
We study how the dynamics of a class of discrete dynamical system models for neuronal networks depends on the connectivity of the network. Specifically, we assume that the network is an Erd\H{o}s-R\'{enyi} random graph and analytically…
A key problem in the modern study of AI is predicting and understanding emergent capabilities in models during training. Inspired by methods for studying reactions in quantum chemistry, we present the ``2-datapoint reduced density matrix".…
The continuous random energy model (CREM) was introduced by Bovier and Kurkova in 2004 which can be viewed as a generalization of Derrida's generalized random energy model. Among other things, their work indicates that there exists a…
We derive an estimate of statistical error in calculating the trace of a large matrix by using random vector, and show that {\em random phase vector} gives the results with the smallest statistical error for a given basis set. This result…
We consider a model of directed polymers on regular trees with complex-valued random weights introduced by Cook and Derrida [CD90] and studied mathematically by Derrida, Evans and Speer [DES93]. In addition to the usual weak-disorder and…
For random matrices with tree-like structure there exists a recursive relation for the local Green functions whose solution permits to find directly many important quantities in the limit of infinite matrix dimensions. The purpose of this…
In this paper, a model for understanding the effects of selection using systems- level computational approaches is introduced. A number of concepts and principles essential for understanding the motivation for constructing the model will be…
It is well-known that one of the most interesting and challenging problems of General Relativity is the energy and momentum localization. There are many attempts to evaluate the energy distribution in a general relativistic system. One of…
Renewable energy is essential for energy security and global warming mitigation. However, power generation from renewable energy sources is uncertain due to volatile weather conditions and complex equipment operations. To improve…
Random graphs, where the connections between nodes are considered random variables, have wide applicability in the social sciences. Exponential-family Random Graph Models (ERGM) have shown themselves to be a useful class of models for…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
We study Derrida's generalized random energy model in the presence of uniform external field. We compute the fluctuations of the ground state and of the partition function in the thermodynamic limit for all admissible values of parameters.…
Dark matter and dark energy are usually assumed to couple only gravitationally. An extension to this picture is to model dark energy as a scalar field coupled directly to cold dark matter. This coupling leads to new physical effects, such…
We give a Large Deviation Principle (LDP) with explicit rate function for the distribution of vertex degrees in plane trees, a combinatorial model of RNA secondary structures. We calculate the typical degree distributions based on nearest…
A discussion is presented of the estimates of the energy and width of resonances in constituent models, with focus on the tetraquark states containing heavy quarks.