We study the joint asymptotic behavior of the space requirement and the total path length (either summing over all root-key distances or over all root-node distances) in random m-ary search trees. The covariance turns out to exhibit a change of asymptotic behavior: it is essentially linear when 3 6 m 6 13 but becomes of higher order when m > 14. Surprisingly, the corresponding asymptotic correl...

The Gilbert-Varshamov (GV) lower bound on the maximum cardinality of a q-ary code of length n with minimum Hamming distance at least d can be obtained by application of Turán’s theorem to the graph with vertex set {0, 1, . . . , q − 1}n in which two vertices are joined if and only if their Hamming distance is at least d. We generalize the GV bound by applying Turán’s theorem to the graph with v...

This paper provides an extensive study of the behavior of the best achievable rate (and other related fundamental limits) in variable-length lossless compression. In the non-asymptotic regime, the fundamental limits of fixed-to-variable lossless compression with and without prefix constraints are shown to be tightly coupled. Several precise, quantitative bounds are derived, connecting the distr...

This article concerns maximum likelihood estimation for discrete time homogeneous nonparametric semi-Markov models with finite state space. In particular, we present the exact maximum likelihood estimator of the semi-Markov kernel which governs the evolution of the semi-Markov chain. We study its asymptotic properties in the following cases: (i) for one observed trajectory, when the length of t...

Consider a family of graphs having a fixed girth and a large size. We give an optimal lower asymptotic bound on the number of even cycles of any constant length, as the order of the graphs tends to infinity.

We establish distributional limit theorems for the shape statistics of a concave majorant (i.e. fluctuations its length, supremum, time it is attained and value at T) Lévy process on [0,T] as T→∞. The scale length other statistics, well their asymptotic dependence, vary significantly with tail behaviour measure. key tool in proofs recent representation all processes using stick-breaking represe...

Among the recent advances in the area of low-density parity-check (LDPC) codes, protograph-based LDPC codes have the advantages of a simple design procedure and highly structured encoders and decoders. These advantages can also be exploited in the design of protograph-based generalized LDPC (G-LDPC) codes. In this dissertation we provide analytical tools which aid the design of protographbased ...

here, a predator-prey model with hassell-varley type functional responses is studied. some sufficient conditions are obtained for the permanence and global asymptotic stability of the system by using comparison theorem and constructing a suitable lyapunov functional. moreover, an example is illustrated to verify the results by simulation.

We investigate the asymptotic decay of the total correlation function h (1,2) in molecular fluids. To this end, we expand the angular dependence of h (1,2) and the direct correlation function c (1,2) in the Ornstein-Zernike equation in a complete set of rotational invariants. We show that all the harmonic expansion coefficients h l1l2l) (r) are governed by a common exponential decay length and ...