Related papers: Diagonal Compressed Random Variables in a Graph W*…
In this paper, we will consider the free probabilistic information about compressed random variables in a graph W*-Probability space. Recall the diagonal compressed random variables in a graph W*-probability space. In particular, we can see…
In [16], we observed the graph W*-probability theory. In this paper, we will review [16] and introduce special amalgamated random variables in this amalgamated W*-probability space. In particular, we will observe the amalgamated…
We investigate the Brown measures of compressions of $R$-diagonal random variables, extending previous results to include unbounded cases. For random variables with finite variance, we demonstrate that the Brown measures of their…
In this paper, we will use the graph W*-probability technique to re-compute the moments and cumulants of the operator which is the N-free sum of semicircular elements. This computation is well-known, but I used the graph probability…
Consider the setting of \emph{randomly weighted graphs}, namely, graphs whose edge weights are chosen independently according to probability distributions with finite support over the non-negative reals. Under this setting, properties of…
We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints. We focus on the setting where this conditional probability is a…
Diagonalizability plays an important role in the analysis and design of multivariable systems. A structured matrix is called structurally diagonalizable if almost all of its numerical realizations, obtained by assigning real values to its…
In this paper, we will consider the graph w*-probability theory.
This paper will be devoted to study weighted (deformed) free Poisson random variables from the viewpoint of orthogonal polynomials and statistics of non-crossing partitions. A family of weighted (deformed) free Poisson random variables will…
We consider a discrete latent variable model for two-way data arrays, which allows one to simultaneously produce clusters along one of the data dimensions (e.g. exchangeable observational units or features) and contiguous groups, or…
In this work we introduce Dynamic Random Geometric Graphs as a basic rough model for mobile wireless sensor networks, where communication distances are set to the known threshold for connectivity of static random geometric graphs. We…
We introduce probability-graphons which are probability kernels that generalize graphons to the case of weighted graphs. Probability-graphons appear as the limit objects to study sequences of large weighted graphs whose distribution of…
Consider a random graph process with $n$ vertices corresponding to points $v_{i} \sim {Unif}[0,1]$ embedded randomly in the interval, and where edges are inserted between $v_{i}, v_{j}$ independently with probability given by the graphon…
We present a new notion of limits of weighted directed graphs of growing size based on convergence of their random quotients. These limits are specified in terms of random exchangeable measures on the unit square. We call our limits…
We study the spatial Gibbs random graphs introduced in [MV16] from the point of view of local convergence. These are random graphs embedded in an ambient space consisting of a line segment, defined through a probability measure that favors…
In this paper, we derive closed-form exact expressions for the main statistics of the ratio of squared alpha-mu random variables, which are of interest in many scenarios for future wireless networks where generalized distributions are more…
Finding a suitable measurement matrix is an important topic in compressed sensing. Though the known random matrix, whose entries are drawn independently from a certain probability distribution, can be used as a measurement matrix and…
Deep Gaussian processes provide a flexible approach to probabilistic modelling of data using either supervised or unsupervised learning. For tractable inference approximations to the marginal likelihood of the model must be made. The…
In this work we give precise asymptotic expressions on the probability of the existence of fixed-size components at the threshold of connectivity for random geometric graphs.
The $W$-random graphs provide a flexible framework for modeling large random networks. Using the Large Deviation Principle (LDP) for $W$-random graphs from [9], we prove the LDP for the corresponding class of random symmetric…