OWPS's next session will be on Wednesday the 1s of March of from 15:00 to 17:00 UTC. Our next speakers are:

Alan Hammond (Berkeley) and Tyler J. Helmuth (Durham University)

Title, abstract and the zoom link are below the signature and can be found on the website https://www.owprobability.org/one-world-probability-seminar.

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With best wishes, Alberto Chiarini (Padua) and Adrián González Casanova (Berkeley and México)

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Talk 1 : Alan Hammond (Berkeley)

Title : Stake-governed random-turn games

Abstract :

Many combinatorial games, such as chess, Go and Hex, are zero-sum games in which two players alternate in making moves. In a random turn variant, each player wins the right to move at any given turn according to the flip of a fair coin. In 2007, Peres, Schramm, Sheffield and Wilson [PSSW] found explicit optimal strategies for a broad class of random-turn games, including Hex (which remains unsolved in its alternating-turn form on the 11-by-11 boards in which it is often played in tournaments). In this talk, we discuss stake-governed random-turn games, introduced recently in joint work with Gábor Pete. Two players of Hex are each given a certain limited budget at the outset of the game. At each turn, each stakes some part of what remains of her budget. The ensuing turn is random, with a player winning the right to move according to the proportion that her stake composes of the total stake at the turn. How much should a player stake at any given turn? Opposing pressures compete: stake too little, and lose the turn; too much, and be left with too little for later in the game. So this question concerns how to evaluate the relative strategic importance of intermediate positions in multi-turn games. We answer it for a class of games that are cousins of the random tug-of-war games introduced by PSSW in 2009; these authors forged a connection between game theory and the infinity Laplacian (which is an L^\infty counterpart to the usual L^2 Laplacian), and we will see how, in a discrete context at least, this connection extends to stake-governed random-turn games.

Talk 2 : Tyler J. Helmuth (Durham University)

Title : The Arboreal Gas

Abstract :

In Bernoulli bond percolation each edge of a graph is declared open with probability p, and closed otherwise. Typically one asks questions about the geometry of the random subgraph of open edges. The arboreal gas is the probability measure obtained by conditioning on the event that the percolation subgraph is a forest, i.e., contains no cycles. Physically, this is a model for studying the gelation of branched polymers. What are the percolative properties of these random forests? Do they contain giant trees? I will discuss what is known and conjectured.

Zoom-link: https://unipd.zoom.us/j/88156851546?pwd=a1NPSkYxRlZoV3dYeERSY3NkV3kvUT09 Meeting ID: 881 5685 1546 
Passcode: 718658

If you are having trouble with zoom, or if the capacity of the zoom room gets exceeded, you can also access to the Youtube live stream at the channel of the seminar: https://www.youtube.com/channel/UCiLiEQGTp6bZEhuHDM-WNWQ