OICC Press Communications in Nonlinear Analysis 2371-7920 4 2 2025 11 09 Randomness of Lacunary statistical acceleration convergence of χ3 over p-­metric spaces defined by Orlicz functions EN Natarajan Rajagopal Department of Mathematics, SASTRA Deemed University, Thanjavur-613 401, India. Nagarajan Subramanian Department of Mathematics, SASTRA Deemed University,Thanjavur-613 401, India. Pannirselvam Thirunavukkarasu P.G. and Research Department of Mathematics, Periyar E.V.R. College (Autonomous),Tiruchirappalli{620 023, India. Journal Article 2025 11 09 In this article, the notion of Randomness of Lacunary statistical acceleration convergence of χ3 over p-metric spaces dened by a sequence of Orlicz has been introduced and some theorems related to that concept have been established using four-dimensional matrix transformations. Author's construction with new definitions and also a new statement of theorems of proofs are formulated.  Analytic sequence double sequences χ3 space Musielak-Orlicz function random p-metric space lacunary sequence statistical convergence converging faster converging at the same rate acceleration eld triple natural density