arXiv subjects

Ron Solan

Publications and source records attributed to Ron Solan.

3 recordsLinked to original sources

arXiv2026

About a ball removal process on bins

We consider a basic balls-and-bins question in which you have to distribute $n$ balls into $k$ bins. Then, round by round, a ball is removed from a non-empty bin chosen uniformly at random. The process ends when a single non-empty bin remains. The goal is to minimize the expected number of remaining balls. An open problem posed by Will Ma asks whether the initial assignment that minimizes the expected number of remaining balls is one that is as balanced as possible. Using a coupling argument, we answer this conjecture positively, and we discuss the case of non-uniform choice among the non-empty bins.

math.PR↗

arXiv2025

An exact tau-leaping method

The Gillespie algorithm and its extensions are commonly used for the simulation of chemical reaction networks. A limitation of these algorithms is that they have to process and update the system after every reaction, requiring significant computation. Another class of algorithms, based on the tau-leaping method, is able to simulate multiple reactions at a time at the cost of decreased accuracy. We present a new algorithm for the exact simulation of chemical reaction networks that is capable of sampling multiple reactions at a time via a first-order approximation similarly to the tau-leaping methods. We prove that the algorithm has an improved runtime complexity compared to existing methods for the exact simulation of chemical reaction networks, and present an efficient and easy to use implementation that outperforms existing methods in practice.

q-bio.MN↗

arXiv2018

Jointly Controlled Lotteries with Biased Coins

We provide a mechanism that uses two biased coins and implements any distribution on a finite set of elements, in such a way that even if the outcomes of one of the coins is determined by an adversary, the final distribution remains unchanged. We apply this result to show that every quitting game in which at least two players have at least two continue actions has an undiscounted $\ep$-equilibrium, for every $\ep > 0$.

math.PR↗