**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

In this article, the notion of Randomness of Lacunary statistical acceleration convergence of \(\chi^{3}\) over \(p\)-metric spaces defined by 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 new statement of theorems of proofs are formulated.

Analytic sequence, double sequences \sep \(\chi^{3}\) space, Musielak-Orlicz function, random \(p\)-metric space, lacunary sequence, statistical convergence, converging faster, converging at the same rate, acceleration field, triple natural density

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