Related papers: Triggered urn models for frequently asked question…
The aim of this paper is to study the asymptotic behavior of strongly reinforced interacting urns with partial memory sharing. The reinforcement mechanism considered is as follows: draw at each step and for each urn a white or black ball…
We study a networked system of innovation processes, where each process is modeled as an urn with infinitely many colors-a classical framework for capturing the emergence of novelties. Extending this paradigm, we analyze a model of…
We consider an urn model with multiple drawing and random time-dependent addition matrix. The model is very general with respect to previous literature: the number of sampled balls at each time-step is random, the addition matrix has…
We complete the study of the model introduced in [11]. It is a two-color urn model with multiple drawing and random (non-balanced) time-dependent reinforcement matrix. The number of sampled balls at each time-step is random. We identify the…
The random self-reinforcement mechanism, characterized by the principle of ``the rich get richer'', has demonstrated significant utility across various domains. One prominent model embodying this mechanism is the random reinforcement urn…
Interacting urns with exponential reinforcement were introduced and studied in Launay (2011). As its parameter $\rho$ tends to $\iy$, this reinforcement mechanism converges to the "generalized" reinforcement, in which the probability of…
This paper studies a very general urn model stimulated by designs in clinical trials, where the number of balls of different types added to the urn at trial n depends on a random outcome directed by the composition at trials 1,2,...,n-1.…
Systems driven by innovation, a pivotal force in human society, present various intriguing statistical regularities, from the Heaps' law to logarithmic scaling or somewhat different patterns for the innovation rates. The Urn Model with…
We consider interacting urns on a finite directed network, where both sampling and reinforcement processes depend on the nodes of the network. This extends previous research by incorporating node-dependent sampling and reinforcement. We…
Consider a finite undirected graph and place an urn with balls of two colours at each vertex. At every discrete time step, for each urn, a fixed number of balls are drawn from that same urn with probability $p$, and from a randomly chosen…
In this work we introduce a new type of urn model with infinite but countable many colors indexed by an appropriate infinite set. We mainly consider the indexing set of colors to be the $d$-dimensional integer lattice and consider balanced…
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…
Consider the multicolored urn model where, after every draw, balls of the different colors are added to the urn in a proportion determined by a given stochastic replacement matrix. We consider some special replacement matrices which are not…
We consider a variant of the randomly reinforced urn where more balls can be simultaneously drawn out and balls of different colors can be simultaneously added. More precisely, at each time-step, the conditional distribution of the number…
We discuss probability text models and their modifications. We construct processes of different and unique words in a text. The models are to correspond to the real text statistics. The infinite urn model (Karlin model) and the Simon model…
The Generalized P\'{o}lya Urn (GPU) is a popular urn model which is widely used in many disciplines. In particular, it is extensively used in treatment allocation schemes in clinical trials. In this paper, we propose a sequential…
We study a system of interacting reinforced random walks defined on polygons. At each stage, each particle chooses an edge to traverse which is incident to its position. We allow the probability of choosing a given edge to depend on the sum…
A central question in random matrix theory is universality. When an emergent phenomena is observed from a large collection of chosen random variables it is natural to ask if this behavior is specific to the chosen random variable or if the…
We introduce a class of reinforcement models where, at each time step $t$, one first chooses a random subset $A_t$ of colours (independent of the past) from $n$ colours of balls, and then chooses a colour $i$ from this subset with…
Consider a number, finite or not, of urns each with fixed capacity $r$ and balls randomly distributed among them. An overflow is the number of balls that are assigned to urns that already contain $r$ balls. When $r=1$, using analytic…