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In this paper, first-passage probability of Markov chains is used to get a strict proof of the existence of degree distribution of the LCD model presented by Bollobas (Random Structures and Algorithms 18(2001)). Also, a precise expression of degree distribution is presented.
In this paper, we give a new method for constructing LCD codes. We employ group rings and a well known map that sends group ring elements to a subring of the $n times n$ matrices to obtain LCD codes. Our construction method guarantees that our LCD co
We investigate the stability condition of redundancy-$d$ multi-server systems. Each server has its own queue and implements popular scheduling disciplines such as First-Come-First-Serve (FCFS), Processor Sharing (PS), and Random Order of Service (ROS
Possible reasons for the uniqueness of the positive geometric law in the context of stability of random extremes are explored here culminating in a conjecture characterizing the geometric law. Our reasoning comes closer in justifying the geometric la
While many questions in (robust) finance can be posed in the martingale optimal transport (MOT) framework, others require to consider also non-linear cost functionals. Following the terminology of Gozlan, Roberto, Samson and Tetali this corresponds t
Let $mathbf{X}$ be a random variable uniformly distributed on the discrete cube $left{ -1,1right} ^{n}$, and let $T_{rho}$ be the noise operator acting on Boolean functions $f:left{ -1,1right} ^{n}toleft{ 0,1right} $, where $rhoin[0,1]$ is the noise