The physiological heart rate is not deterministic but rather varies in time; those variations are termed heart rate variability (HRV). It is well known that low HRV is often seen in patients prone to arrhythmias. The ability of HRV to predict arrhythmia events is traditionally attributed to an impaired balance between the autonomic sympathetic and parasympathetic tone. However, there is no concrete model that directly relates low HRV to the electrical conduction in the cardiac tissue and to arrhythmogenic dynamic properties. We simulated stochastic cardiac pacing with Gaussian distribution using 2D human ventricular tissue model. Conduction stabilization was obtained with stochastic pacing owing to reduced propensity of the appearance of action potential duration (APD) discordant alternans and reduced APD spatial heterogeneity.