arXiv subjects

S. Foss

Publications and source records attributed to S. Foss.

4 recordsLinked to original sources

arXiv2020

Limit theorems for the maximal path weight in a directed graph on the line with random weights of edges

We consider the infinite directed graph with vertices the set of integers ...,-2,-1,0,1,2,... . Let v be a random variable taking either finite values or value "minus infinity". Consider random weights v(j,k), indexed by pairs (j,k) of integers with j 0)>0, the conditional distribution of v, given v>0, is not degenerate, and that E exp(Cv) is finite, for some C>0. We derive local limit theorems in the normal and moderate large deviations regimes in the case where v has an arithmetic distribution. We also derive an integro-local theorem in the case where v has a non-lattice distribution.

math.PR↗

arXiv2013

Asymptotics for sums of random variables with local subexponential behaviour

We study distributions $F$ on $[0,\infty)$ such that for some $T\le\infty$, $F^{*2}(x,x+T]\sim 2 F(x,x+T]$. The case $T=\infty$ corresponds to $F$ being subexponential, and our analysis shows that the properties for $T<\infty$ are, in fact, very similar to this classical case. A parallel theory is developed in the presence of densities. Applications are given to random walks, the key renewal theorem, compound Poisson process and Bellman-Harris branching processes.

math.PR↗

arXiv2013

Tail asymptotics for the supremum of a random walk when the mean is not finite

We consider the sums $S_n=ξ_1+\cdots+ξ_n$ of independent identically distributed random variables. We do not assume that the $ξ$'s have a finite mean. Under subexponential type conditions on distribution of the summands, we find the asymptotics of the probability ${\bf P}\{M>x\}$ as $x\to\infty$, provided that $M=\sup\{S_n,\ n\ge1\}$ is a proper random variable. Special attention is paid to the case of tails which are regularly varying at infinity. We provide some sufficient conditions for the integrated weighted tail distribution to be subexponential. We supplement these conditions by a number of examples which cover both the infinite- and the finite-mean cases. In particular, we show that subexponentiality of distribution $F$ does not imply subexponentiality of its integrated tail distribution $F^I$.

math.PR↗

arXiv2007

A Comparison between 1.5$μ$m Photoluminescence from Er-Doped Si-Rich Sio2 Films and (Er,Ge) Co-Doped Sio2 Films

We have studied the 1.5 $μ$m photoluminescence (PL) from Er ions after annealing two different sample sets in the temperature range 500 °C to 1100 °C. The different sample sets were made by magnetron sputtering from composite targets of Si+SiO2+Er and Ge+SiO2+Er respectively for the different sample sets. The annealing induces Si - and Ge-nanoclusters respectively in the different film sets. The PL peak reaches its maximum intensity after annealing at 700 °C for samples with Ge nanoclusters and after annealing at 800 °C for samples with Si. No luminescence from nanoclusters was detected in neither sample sets. This is interpreted as an energy transfer from the nanocluster to Er atoms. Transmission electron microscopy shows that after annealing to the respective temperature yielding the maximum PL intensity both the Ge and Si clusters are non-crystalline. Here we mainly compare the spectral shape of Er luminescence emitted in these different nanostructured matrixes. The PL spectral shapes are clearly different and witness a different local environment for the Er ions.

cond-mat.mtrl-sci↗