We study limiting distributions of exponential sums SN (t) = âˆ‘N i=1 e tXi as t â†’ âˆž, N â†’ âˆž, where(Xi) are i.i.d. random variables. Two cases are considered: (A) ess sup Xi = 0 and (B) ess sup Xi = âˆž.â€¦ (More)

Consider the set Ln of convex polygons Î“ with vertices on the integer lattice Z, non-negative inclination of the edges and fixed endpoints 0 = (0, 0) and n = (n1, n2). We study the asymptoticâ€¦ (More)

We study the limiting distribution of the sum SN (t) = âˆ‘N i=1 e tXi as t â†’âˆž, N â†’âˆž, where (Xi) are i.i.d. random variables. Attention to such exponential sums has been motivated by various problems inâ€¦ (More)

We consider the occupancy problem where balls are thrown independently at infinitely many boxes with fixed positive frequencies. It is well known that the random number of boxes occupied by the firstâ€¦ (More)

We consider a continuous-time branching random walk on the lattice Z (d â‰¥ 1) evolving in a random branching environment. The motion of particles proceeds according to the law of a simple symmetricâ€¦ (More)

The distributionÎ¼cl of a Poisson cluster process in X = Rd (with i.i.d. clusters) is studied via an auxiliary Poisson measure on the space of configuratio ns inX = âŠ”nX, with intensity defined as aâ€¦ (More)

We consider a continuous-time branching random walk on the integer lattice Zd (d > 1) with a finite number of branching sources, or catalysts. The random walk is assumed to be spatially homogeneousâ€¦ (More)

The distribution Î¼ of a Poisson cluster process in X = R (with n-point clusters) is studied via the projection of an auxiliary Poisson measure in the space of configurations in X, with the intensityâ€¦ (More)

Abstract. The distribution Î¼ of a Gibbs cluster point process in X = R (with n-point clusters) is studied via the projection of an auxiliary Gibbs measure defined on the space of configurations in Xâ€¦ (More)