Why are financial balances heavy-tailed? The rich have vastly more than the typical person, and the distribution has a long tail extending to extreme wealth. Standard explanations invoke network effects (the rich get richer through preferential attachment), institutional structures (inheritance, capital gains), or multiplicative processes (returns compound).
Mattsson et al. (arXiv:2602.20713) produce heavy tails from something simpler: random walks on a temporal network with conserved funds and heterogeneous spending propensities. People receive money and spend money. The amounts and timing follow a random walk on a network that changes over time. The only required ingredient for heavy tails is that people differ in how readily they spend.
The model enforces fund conservation — money moves, it doesn't appear or disappear. Transactions happen on an activity-driven temporal network — people become active at different rates and transact with whoever else is active. The spending propensity — the fraction of available funds a person sends per transaction — varies across individuals. Some people spend readily. Others hold. This variance alone produces heavy-tailed distributions for both balances and transaction sizes.
The mechanism: a person with low spending propensity accumulates funds during transactions, building a larger balance. That larger balance means their occasional transactions are larger. The heterogeneity of propensity drives the heterogeneity of outcome, through the accumulation dynamics of a conserved quantity on a network. No preferential attachment. No compound returns. No institutional structure. Just different people spending at different rates, with money that must go somewhere.
Calibrated against empirical data from a closed digital currency community, the model also reproduces the observed correlation between inflows and outflows — people who receive more also spend more, but the relationship is not one-to-one. The spending propensity breaks the symmetry: high-propensity spenders pass money through quickly; low-propensity holders accumulate it.
The deepest point: the heavy tail is not caused by the network, the dynamics, or the initial conditions. It is caused by the diversity of the agents. Identical agents on the same network produce thin-tailed distributions. Heterogeneous agents produce fat tails. The inequality is in the propensities, not the process.