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The sensitivities revealed by a sensitivity analysis of a probabilistic network typically depend on the entered evidence. For a real-life network therefore, the analysis is performed a number of times, with different evidence. Although…
We study the characteristic function and moments of the integer-valued random variable $\lfloor X+\alpha\rfloor$, where $X$ is a continuous random variables. The results can be regarded as exact versions of Sheppard's correction. Rounded…
Probabilistic concurrent/distributed strategies have so far not been investigated thoroughly in the context of imperfect information, where the Player has only partial knowledge of the moves made by the Opponent. In a situation where the…
A two-type version of the frog model on $\mathbb{Z}^d$ is formulated, where active type $i$ particles move according to lazy random walks with probability $p_i$ of jumping in each time step ($i=1,2$). Each site is independently assigned a…
We introduce a family of probabilistic {\it scale-invariant} Leibniz-like pyramids and $(d+1)$-dimensional hyperpyramids ($d=1,2,3,...$), characterized by a parameter $\nu>0$, whose value determines the degree of correlation between $N$…
We study analytically the asymptotic behaviour of the average probability P(n,t) for the trajectory of a 2D Brownian particle wandering in the presence of randomly distributed traps to wind n times around a given point after a time t. It is…
We study an urn process with two urns, initialized with a ball each. Balls are added sequentially, the urn being chosen independently with probability proportional to the $\alpha^{th}$ power $(\alpha >1)$ of the existing number of balls. We…
The paper reviews some axioms of additivity concerning ranking methods used for generalized tournaments with possible missing values and multiple comparisons. It is shown that one of the most natural properties, called consistency, has…
The cooperative behaviour of interacting neurons and synapses is studied using models and methods from statistical physics. The competition between training error and entropy may lead to discontinuous properties of the neural network. This…
Let P_{n,m} denote the graph taken uniformly at random from the set of all planar graphs on {1,2,..., n} with exactly m(n) edges. We use counting arguments to investigate the probability that P_{n,m} will contain given components and…
Within a contest there is some probability M_i(t) that contestant i will be the winner, given information available at time t, and M_i(t) must be a martingale in t. Assume continuous paths, to capture the idea that relevant information is…
A well-studied randomized election algorithm proceeds as follows: In each round the remaining candidates each toss a coin and leave the competition if they obtain heads. Of interest is the number of rounds required and the number of…
We introduce a counting process to model the random occurrence in time of car traffic accidents, taking into account some aspects of the self-excitation typical of this phenomenon. By combining methods from probability and differential…
Several resource allocation settings involve agents with unequal entitlements represented by weights. We analyze weighted fair division from an asymptotic perspective: if $m$ items are divided among $n$ agents whose utilities are…
In this paper, we consider a multi-drawing urn model with random addition. At each discrete time step, we draw a sample of m balls. According to the composition of the drawn colors, we return the balls together with a random number of balls…
The probability density function of single-point velocity fluctuations in turbulence is studied systematically using Fourier coefficients in the energy-containing range. In ideal turbulence where energy-containing motions are random and…
We experimentally evaluate the comparative performance of the winner-bid, average-bid, and loser-bid auctions for the dissolution of a partnership. The analysis of these auctions based on the empirical equilibrium refinement of Velez and…
We consider a decentralized stochastic multi-armed bandit problem with multiple players. Each player aims to maximize his/her own reward by pulling an arm. The arms give rewards based on i.i.d. stochastic Bernoulli distributions. Players…
Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of…
Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a…