Related papers: Jackpot statistics, a physicist's approach
Local convergence techniques have become a key methodology to study sparse random graphs. However, convergence of many random graph properties does not directly follow from local convergence. A notable, and important, such random graph…
The proposition of lottery ticket hypothesis revealed the relationship between network structure and initialization parameters and the learning potential of neural networks. The original lottery ticket hypothesis performs pruning and weight…
We put forward a conjecture of recurrence for a gas of hard spheres that collide elastically in a finite volume. The dynamics consists of a sequence of instantaneous binary collisions. We study how the numbers of collisions of different…
The focal point of this paper is the so-called Kelly Criterion, a prescription for optimal resource allocation among a set of gambles which are repeated over time. The criterion calls for maximization of the expected value of the…
In the online prediction framework, we use generalized entropy of to study the loss rate of predictors when outcomes are drawn according to stationary ergodic distributions over the binary alphabet. We show that the notion of generalized…
We consider time-dependent space isotropic and time stationary spherical Gaussian random fields. We establish Chung's law of the iterated logarithm and solve the small probabilities problem. Our results depend on the high-frequency…
We present a simple model of Texas hold'em poker tournaments which retains the two main aspects of the game: i. the minimal bet grows exponentially with time; ii. players have a finite probability to bet all their money. The distribution of…
Winner-take-all phenomena are observed in various competitive systems. We find similar phenomena in replicator models with randomly fluctuating growth rates. The disparity between winners and losers increases indefinitely, even if all…
Motivated by applications to data networks where fast convergence is essential, we analyze the problem of learning in generic N-person games that admit a Nash equilibrium in pure strategies. Specifically, we consider a scenario where…
We give a criterion under which the expected return on a ticket for certain large lotteries is positive. In this circumstance, we use elementary portfolio analysis to show that an optimal investment strategy includes a very small allocation…
Simple stochastic games are two-player zero-sum stochastic games with turn-based moves, perfect information, and reachability winning conditions. We present two new algorithms computing the values of simple stochastic games. Both of them…
Consider a gambling game in which we are allowed to repeatedly bet a portion of our bankroll at favorable odds. We investigate the question of how to minimize the expected number of rounds needed to increase our bankroll to a given target…
With increasing game size, a problem of computational complexity arises. This is especially true in real world problems such as in social systems, where there is a significant population of players involved in the game, and the complexity…
A fast algorithm to study one-dimensional self-gravitating systems, and, more generally, systems that are Lagrangian integrable between collisions, is presented. The algorithm is event-driven, and uses a heap-ordered set of predicted future…
Linear quadratic graphon field games (LQ-GFGs) are defined to be LQ games which involve a large number of agents that are weakly coupled via a weighted undirected graph on which each node represents an agent. The links of the graph…
Stochastic games are a natural model for the synthesis of controllers confronted to adversarial and/or random actions. In particular, $\omega$-regular games of infinite length can represent reactive systems which are not expected to reach a…
Dynamic game arises as a powerful paradigm for multi-robot planning, for which safety constraint satisfaction is crucial. Constrained stochastic games are of particular interest, as real-world robots need to operate and satisfy constraints…
This paper considers a time-varying game with $N$ players. Every time slot, players observe their own random events and then take a control action. The events and control actions affect the individual utilities earned by each player. The…
Sequences of repeated gambles provide an experimental tool to characterize the risk preferences of humans or artificial decision-making agents. The difficulty of this inference depends on factors including the details of the gambles offered…
In economy, markets are denoted as efficient when it is impossible to systematically generate profits which outperform the average. In the past years, the concept has been tested in other domains such as the growing sports betting market.…