The main goal of high-energy heavy-ion collisions has been to understand Quantum Chromo Dynamics (QCD) under extreme temperature and baryon densities. At ordinary temperatures, the quarks and gluons are confined within hadrons, but at very high temperatures and densities, we have a deconfined phase of quarks and gluons, the Quark Gluon Plasma (QGP). Over the past years, evidence for the distinct phases of QGP and hadron gas has been established experimentally.

Fluctuations and correlations have been considered as sensitive observables to explore the phases of the strongly interacting QCD matter, namely the QGP phase and the Hadron Gas phase, as they can provide essential information about the effective degrees of freedom. The main goal of this thesis is exploring the critical phenomenon in QCD phase diagram. In this thesis, we have studied two main aspects of the QCD phase diagram, namely, the crossover at small baryon chemical potential and signatures of local parton density fluctuation near the critical point within the framework of the STAR experiment at the Relativistic Heavy Ion Collider (RHIC).

Phase transitions and/or critical phenomena are known to lead to local density fluctuations. In the coalescence mechanism of particle production, the baryon formation probability can be influenced by these local parton density fluctuations, thereby leading to clusters and voids in the phase-space distribution of hadrons. In order to probe the density fluctuation in heavy-ion collisions, we studied the distribution of the ratio of particles in a given angular region to the total number of particles produced. We expect the shape of this distribution to be sensitive to clustering in phase space. For the first part, we measured the cumulants of this self-normalized distribution using the data from Au+Au collisions from the STAR Beam Energy Scan program to probe baryon density fluctuations.

Lattice QCD is a well-established non-perturbative approach to solve the theory of quarks and gluons exactly from first principles. However, these calculations are exact only at zero baryon chemical potential ($\mu_B$). In order to explore the phenomenon at finite $\mu_B$, these calculations are extended using Taylor expansion about $\mu_B = 0$. A constraint on the equation of state from Lattice QCD can be achieved by using the ratio of the sixth-order to the second-order baryon susceptibilities. In addition, Lattice QCD also predicts that the ratio of the sixth-order to second-order cumulants of baryon number remains negative at the chiral transition temperature. For the second part, we measured of the sixth-order cumulant for the net-proton (proxy for net-baryon) multiplicity distribution for Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV (which corresponds to $\mu_B \sim 20$ MeV) for the high statistics run in the year 2014.

Unfortunately, the higher-order cumulants are very sensitive to experimental artifacts that one has to deal with in the analysis of heavy-ion collision data. The factorial moment method, which is used to account for the effect of detector efficiency, assumes the underlying detector response function to be a Binomial distribution. In order to account for non-Binomial detector responses and multiplicity-dependent efficiency, we developed an unfolding approach to measure efficiency-corrected higher-order cumulants of event-by-event distribution of physical variables.