In the talk I give a review of few different problems which can be
analyzed using the image of a sequential ballistic deposition (BD) in
a finite box.
The first problem deals with the statistics of mutually interweaved
directed random walks (i.e. random braids). Such model system has very
broad application area ranging from entangled nematic-like textures to
topological aspects of vortex glasses in superconductors.
Reformulating BD on a group-theoretic language, we develop a symbolic
dynamics which permits us to construct the objects with a braid-like
topology in 1+1 and in 2+1 dimension and to solve the simplest
statistical-topological problems where the noncommutative character of
entanglements is properly taken into account.
In the second part of the talk I discuss an analytic approach to
the statistics of the longest common subsequence (LCS) of a pair of
random sequences drawn from the alphabet with c letters, a challenging
problem in computational evolutionary biology. We have shown that in
the limit c>>1 this problem can be mapped to the 2+1-dimensional
directed percolation, which in turn corresponds to the search of the
longest increasing subsequence (LIS) in a random sequence of integers.
The last problem has a straightforward interpretation in terms of the
uniform totally asymmetric ballistic deposition.