Lifting theorems for some classes of two parameter martingales.
Likelihood and parametric heteroscedasticity in normal connected linear models
A linear model in which the mean vector and covariance matrix depend on the same parameters is connected. Limit results for these models are presented. The characteristic function of the gradient of the score is obtained for normal connected models, thus, enabling the study of maximum likelihood estimators. A special case with diagonal covariance matrix is studied.
Likely path to extinction in simple branching models with large initial population.
Liminf behaviours of the windings and Lévy's stochastic areas of planar brownian motion
Limit distribution for 1-dimensional diffusion in a reflected brownian medium
Limit distribution of the time of coincidence in renewal streams
Limit distributions and random trees derived from the birthday problem with unequal probabilities.
Limit distributions for multitype branching processes of -ary search trees
Let be an integer. The so-called-ary search treeis a discrete time Markov chain which is very popular in theoretical computer science, modelling famous algorithms used in searching and sorting. This random process satisfies a well-known phase transition: when , the asymptotic behavior of the process is Gaussian, but for it is no longer Gaussian and a limit of a complex-valued martingale arises. In this paper, we consider the multitype branching process which is the continuous time version...
Limit distributions for queues and random rooted trees.
Limit distributions for sums of shrunken random variables [Book]
Limit laws for a coagulation model of interacting random particles
Limit laws for products of free and independent random variables
We determine the distributional behavior of products of free (in the sense of Voiculescu) identically distributed random variables. Analogies and differences with the classical theory of independent random variables are then discussed.
Limit laws for Random matrices and free products.
Limit laws for the energy of a charged polymer
In this paper we obtain the central limit theorems, moderate deviations and the laws of the iterated logarithm for the energy Hn=∑1≤j<k≤nωjωk1{Sj=Sk} of the polymer {S1, …, Sn} equipped with random electrical charges {ω1, …, ωn}. Our approach is based on comparison of the moments between Hn and the self-intersection local time Qn=∑1≤j<k≤n1{Sj=Sk} run by the d-dimensional random walk {Sk}. As partially needed for our main objective and partially motivated by their independent interest,...
Limit laws for transient random walks in random environment on
We consider transient random walks in random environment on with zero asymptotic speed. A classical result of Kesten, Kozlov and Spitzer says that the hitting time of the level converges in law, after a proper normalization, towards a positive stable law, but they do not obtain a description of its parameter. A different proof of this result is presented, that leads to a complete characterization of this stable law. The case of Dirichlet environment turns out to be remarkably explicit.
Limit laws of transient excited random walks on integers
We consider excited random walks (ERWs) on ℤ with a bounded number of i.i.d. cookies per site without the non-negativity assumption on the drifts induced by the cookies. Kosygina and Zerner [15] have shown that when the total expected drift per site, δ, is larger than 1 then ERW is transient to the right and, moreover, for δ>4 under the averaged measure it obeys the Central Limit Theorem. We show that when δ∈(2, 4] the limiting behavior of an appropriately centered and scaled excited random...
Limit Measures on Compact Semitopological Semigroups.
Limit Measures Related to the Conditionally Free Convolution
We describe the limit measures for some class of deformations of the free convolution, introduced by A. D. Krystek and Ł. J. Wojakowski. In particular, we provide a counterexample to a conjecture from their paper.
Limit probabilities for random sparse bit strings.
Limit shapes of Gibbs distributions on the set of integer partitions : the expansive case
We find limit shapes for a family of multiplicative measures on the set of partitions, induced by exponential generating functions with expansive parameters, ak∼Ckp−1, k→∞, p>0, where C is a positive constant. The measures considered are associated with the generalized Maxwell–Boltzmann models in statistical mechanics, reversible coagulation–fragmentation processes and combinatorial structures, known as assemblies. We prove a central limit theorem for fluctuations of a properly scaled partition...