Related papers: First Passage Properties of the Polya Urn Process

In this paper we analyze a L\'evy process reflected at a general (possibly random) barrier. For this process we prove Central Limit Theorem for the first passage time. We also give the finite-time first passage probability asymptotics.

For first passage percolation on $\mathbb{Z}^2$ with i.i.d. bounded edge weights, we consider the upper tail large deviation event; i.e., the rare situation where the first passage time between two points at distance $n$, is macroscopically…

The dynamics of passive Brownian tracer particles in steady two-dimensional potential flows between sources and sinks is investigated. The first-passage probability, $p(t)$, exhibits power-law decay with a velocity-dependent exponent in…

Juggling patterns can be described by a closed walk in a (directed) state graph, where each vertex (or state) is a landing pattern for the balls and directed edges connect states that can occur consecutively. The number of such patterns of…

This paper concerns the long term behaviour of a growth model describing a random sequential deposition of particles on a finite graph. The probability of allocating a particle at a vertex is proportional to a log-linear function of numbers…

The first-passage time is proposed as an independent thermodynamic parameter of the statistical distribution that generalizes the Gibbs distribution. The theory does not include the determination of the first passage statistics itself. A…

We consider a game with two piles, in which two players take turn to add $a$ or $b$ chips ($a$, $b$ are not necessarily positive) randomly and independently to their respective piles. The player who collects $n$ chips first wins the game.…

We consider a run-and-tumble particle on a finite interval $[a,b]$ with two absorbing end points. The particle has an internal velocity state that switches between three values $v,0,-v$ at exponential times, thus incorporating positive…

Suppose you and your friend both do $n$ tosses of an unfair coin with probability of heads equal to $\alpha$. What is the behavior of the probability that you obtain at least $d$ more heads than your friend if you make $r$ additional…

We study a general preferential attachment and Polya's urn model. At each step a new vertex is introduced, which can be connected to at most one existing vertex. If it is disconnected, it becomes a pioneer vertex. Given that it is not…

This paper presents necessary and sufficient conditions for on- and off-diagonal transition probability estimates for random walks on weighted graphs. On the integer lattice and on may fractal type graphs both the volume of a ball and the…

There are two methods for counting the number of occurrences of a string in another large string. One is to count the number of places where the string is found. The other is to determine how many pieces of string can be extracted without…

Spontaneous symmetry breaking is a fundamental notion in modern physics, ranging from high energy to condensed matter. However, the usual spontaneous symmetry breaking only considers the equal probability to select the vacua. In this work,…

We consider a particle which moves on the x axis and is subject to a constant force, such as gravity, plus a random force in the form of Gaussian white noise. We analyze the statistics of first arrival at point $x_1$ of a particle which…

We derive exact expressions for the probabilities that partly random hyperplanes separate two Euclidean balls. The probability that a fully random hyperplane separates two balls turns out to be significantly smaller than the corresponding…

Consider an urn filled with balls, each labeled with one of several possible collective decisions. Now, let a random voter draw two balls from the urn and pick her more preferred as the collective decision. Relabel the losing ball with the…

For a one-dimensional Wiener process with stochastic resetting ${\cal X}(t)$, obtained from an underlying Wiener process $X(t),$ we study the statistical properties of its first-passage time through zero, when starting from $x>0,$ and its…

In this work, recent results on the moments of balanced P\'olya urns are generalized to unbalanced urns, with the condition that the expected change in total activity at each step is constant. We also provide applications of our results to…

Sampling permutations from S_n is a fundamental problem from probability theory. The nearest neighbor transposition chain \cal{M}}_{nn} is known to converge in time \Theta(n^3 \log n) in the uniform case and time \Theta(n^2) in the constant…

In two recent works, Kuba and Mahmoud (arXiv:1503.090691 and arXiv:1509.09053) introduced the family of two-color affine balanced Polya urn schemes with multiple drawings. We show that, in large-index urns (urn index between $1/2$ and $1$)…