Related papers: Velocity formulae between entropy and hitting time…

Suppose we are given the free product V of a finite family of finite or countable sets. We consider a transient random walk on the free product arising naturally from a convex combination of random walks on the free factors. We prove the…

We consider a continuous time Markov chain on a countable state space and prove a joint large deviation principle for the empirical measure and the empirical flow, which accounts for the total number of jumps between pairs of states. We…

We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state…

We study the distribution of the number of (non-backtracking) periodic walks on large regular graphs. We propose a formula for the ratio between the variance of the number of $t$-periodic walks and its mean, when the cardinality of the…

While entropy changes are the usual subject of fluctuation theorems, we seek fluctuation relations involving time-symmetric quantities, namely observables that do not change sign if the trajectories are observed backward in time. We find…

Thermalization is one of the most important phenomena in statistical physics. Often, the transition probabilities between different states in the phase space is or can be approximated by constants. In this case, the system can be described…

In the present paper we show that for any given digraph $\mathbb{G} =([n], \vec{E})$, i.e. an oriented graph without self-loops and 2-cycles, one can construct a 1-dependent Markov chain and $n$ identically distributed hitting times $T_1,…

We study convergence to equilibrium for a large class of Markov chains in random environment. The chains are sparse in the sense that in every row of the transition matrix $P$ the mass is essentially concentrated on few entries. Moreover,…

To improve the routing decisions of individual drivers and the management policies designed by traffic operators, one needs reliable estimates of travel time distributions. Since congestion caused by both recurrent patterns (e.g., rush…

A constructive proof is given to the fact that any ergodic Markov chain can be realized as a random walk subject to a synchronizing road coloring. Redundancy (ratio of extra entropy) in such a realization is also studied.

Entropy measures have become increasingly popular as an evaluation metric for complexity in the analysis of time series data, especially in physiology and medicine. Entropy measures the rate of information gain, or degree of regularity in a…

We consider random walks in which the walk originates in one set of nodes and then continues until it reaches one or more nodes in a target set. The time required for the walk to reach the target set is of interest in understanding the…

For a continuous-time quantum walk on a line the variance of the position observable grows quadratically in time, whereas, for its classical counterpart on the same graph, it exhibits a linear, diffusive, behaviour. A quantum walk, thus,…

For random walks on graph $\mathcal{G}$ with $n$ vertices and $m$ edges, the mean hitting time $H_j$ from a vertex chosen from the stationary distribution to vertex $j$ measures the importance for $j$, while the Kemeny constant…

We examine two analytical characterisation of the metastable behavior of a Markov chain. The first one expressed in terms of its transition probabilities, and the second one in terms of its large deviations rate functional. Consider a…

We study ergodic properties of a family of traffic maps acting in the space of bi-infinite sequences of real numbers. The corresponding dynamics mimics the motion of vehicles in a simple traffic flow, which explains the name. Using…

We prove an explicit formula of hitting times in terms of enumerations of spanning trees for random walks on general connected graphs. We apply the formula to improve Lawler's bound of hitting times for general graphs, prove a sharp bound…

We consider a strictly substochastic matrix or an stochastic matrix with absorbing states. By using quasi-stationary distributions one shows there is a canonical associated stationary Markov chain. Based upon $2-$stringing representation of…

Entropy rate is a real valued functional on the space of discrete random sources which lacks a closed formula even for subclasses of sources which have intuitive parameterizations. A good way to overcome this problem is to examine its…

Predictability of behavior has emerged an an important characteristic in many fields including biology, medicine, and marketing. Behavior can be recorded as a sequence of actions performed by an individual over a given time period. This…