Random walks constitute one of the most fundamental models in the study of stochastic processes, representing systems that evolve in a sequence of random steps. Their applications range from modelling ...

Stochastic differential equations (SDEs) and random processes form a central framework for modelling systems influenced by inherent uncertainties. These mathematical constructs are used to rigorously ...

When the mathematicians Jeff Kahn and Gil Kalai first posed their “expectation threshold” conjecture in 2006, they didn’t believe it themselves. Their claim — a broad assertion about mathematical ...

Random processes take place all around us. It rains one day but not the next; stocks and bonds gain and lose value; traffic jams coalesce and disappear. Because they’re governed by numerous factors ...