  Concentration inequalities, which prove to be very useful in a variety of
fields, provide fairly tight bounds for large deviation probability while
central limit theorem (CLT) describes the asymptotic distribution around the
mean (within scope of $\sqrt{n}$ order). Harris (1963) conjectured that for a
supercritical branching random walk (BRW) of i.i.d offspring and iid
displacement, population's positions in $nth$ generation approach to Gaussian
distribution -- central limit theorem. This conjecture was latter proved by
Stam (1966) and Kaplan and Asmussen (1976). Refinements and extensions
followed. Yet little effort is known on large deviation probability for BRW. In
this note, we suggest and verify a more general and probably more formal
setting of BRW. Benefiting from this framework, a Chernoff bound for BRW is
immediately obtained. The relation between RW (random walk) and BRW is
addressed.
