  Proton-Proton ($pp$) collisions at the Large Hadron Collider (LHC) are
simulated in order to study events with a high local density of charged
particles produced in narrow pseudorapidty windows of $\Delta\eta$ = 0.1, 0.2,
and 0.5. The $pp$ collisions are generated at center of mass energies of
$\sqrt{s} = 2.36$, $7$, $8$, and $13$ TeV, i.e. the energies at which the LHC
has operated so far, using PYTHIA and HERWIG event generators. We have also
studied the average of the maximum charged-particle density versus the event
multiplicity for all events, using the different pseudorapidity windows. This
study prepares for the multi-particle production background expected in a
future search for anomalous high-density multiplicity fluctuations using the
LHC data.
