4 papers · 2 filters
Moments approach for the elephant random walk
Pradeep Vishwakarma
We discuss the method of moments for the one-dimensional elephant random walk (ERW). We first derive a differential recurrence relation for the characteristic function of the ERW,…
Convergence of random sums in non-commutative probability
Arup Bose, Pradeep Vishwakarma
Random sums of independent random variables have been extensively studied in classical probability theory. We consider random sums of self-adjoint variables from a non-commutative…
Revisiting Toeplitz and Hankel random matrices via -convergence of circulant-type matrices
Arup Bose, Pradeep Vishwakarma
We establish the joint -convergence of a random circulant matrix and a specific deterministic diagonal matrix. We also show that the empirical spectral distributions of skew-cir…
Some Spatial Point Processes of Poisson Family
Pradeep Vishwakarma
Spatial Poisson point processes on finite-dimensional Euclidean space provide fundamental mathematical tools for modeling random spatial point patterns. In this paper, we introduce…